Evans, a former Wales international, was released from jail last month after serving half of a five-year jail term imposed in April 2012 for raping a 19-year-old woman in a hotel room in Rhyl.
United, his former club, have allowed him to train with their players - and faced strong criticism as a result.
Clegg, MP for Sheffield Hallam, told LBC Radio: “’I think the owners need to think really long and hard about the fact that when you take a footballer on, you are not taking just a footballer these days, you are also taking on a role model.
“You are taking on a role model, particularly for a lot of young boys who look up to their heroes on a football pitch in a team like that, and he has committed a very serious crime.
“It is for the football club to decide, but I really do think that footballers these days, they are major public figures who have a public responsibility to set an example for other people.
“I’m sure that will weigh heavily in the decisions made by the owners of Sheffield United.”
Paul Blomfield, the Labour MP for Sheffield Central who declares ownership of 100 Sheffield United shares on his website, said the Blades’ decision to allow Evans to train with the club was “dragging our name through the mud and dividing fans’’.
Evans’ return was met with outrage by campaign groups, with the group End Violence Against Women Coalition saying it was “appalled”, while DBL Logistics, back-of-the-shirt sponsors for the Blades, said it would withdraw its financial support should Evans be re-signed by the club.
However, team boss Nigel Clough insisted the club was “a long way” from looking to offer the 25-year-old a contract and that it was a request from the Professional Footballers’ Association to allow him the opportunity to rebuild his fitness.
Clough said on Sky Sports News HQ: ‘’I think everything has been deliberated properly, nobody has rushed into any decisions at the club.
“It has been prompted by the PFA and that’s as far as it goes now.
“We deliberated as a club for some weeks and came to this decision. According to the law of the land he is entitled an opportunity to resume his career.”
Asked whether allowing Evans to train at the club would lead to a potential deal at Bramall Lane, Clough added: ‘’That’s a long way from being true. The statement said that he is purely down to train with us and we will take it from there.’’
On the pitch, United were beaten 1-0 at Walsall in the Johnstone’s Paint Trophy, where a small group of Blades fans inside the first 10 minutes sang: “We’ll sign who we want.”
TV presenter Charlie Webster, who revealed in an interview earlier this year that she had been sexually assaulted as a teenager, resigned from her patron role with United on Tuesday, after earlier vowing to quit should Evans be re-signed by United. She was followed yesterday by local businesswoman Lindsay Graham and singer Dave Berry, who also quit their roles as patrons of the club’s charity foundation.
Sheffield Central’s Labour MP Paul Blomfield published an open letter to the club’s co-chairmen Kevin McCabe and Jim Phipps, urging them to reconsider their decision to let the convicted rapist train with their players. In it, he said he’d chosen to break his silence on the issue as, until now, he’d been confident “the right decision” would be made.
Referring to the club’s statement, the lifelong United supporter said: “You rightly say that ‘rape is a heinous crime’ and that you ‘do not question Mr Evans’ conviction’. You also highlight the right to ‘rehabilitation under law’, with which I strongly agree.
“Everybody deserves a second chance, but with such serious offences this is based on offenders recognising the gravity of their crimes and seeking to make good for them. Since his release Ched Evans has not taken this first step towards rehabilitation, but has trivialised his crime by describing it as an “act of infidelity”.
He added that taking Evans back sent a “disturbing message” to both young people and victims of sexual violence.
In an interview with BBC’s Newsnight programme on Tuesday evening, Miss Webster said she had had a conversation with the chairman of the club, which she described as “positive” but she added that she felt she had to make a decision after Evans returned to training.
She said: “My decision is made on the fact that I don’t believe a convicted rapist, as in Ched Evans, should go back to a club that I am patron of and should go back into the community to represent the community.
“He’s not just going into a job, he’s bandied as a role model, we cheer him on as a role model and he’s influencing the next generation of young men who are currently still making their decisions on how to treat women and what sexual mutual consent is.”
Today, Sheffield singer Dave Berry called for “common sense” and said he’d resigned “to make some sort of stand.”
He said: “I know he has served his sentence but he should have shown a bit of remorse, said sorry to the family, maybe made a donation to Rape Crisis charity - all the gestures people can do in this sort of situation.
“The club hasn’t handled it very well. Common sense should be the most important thing.”
Ms Graham, who runs LGL Limited, a firm which specialises in advising on school meals and health, said her reasons for resigning were “personal.”
An appeal against Evans’s conviction was rejected at the Court of Appeal in 2012. His case is due to be looked at by the Criminal Cases Review Commission.
After his release, Evans released a video on his website protesting his innocence