Redfearn confirmed on Thursday that the former Whites favourite is definitely on a list he has handed to president Massimo Cellino identifying possible signings.
Becchio was sold to Norwich City in 2013 but the Argentinian goal-getter has made little impact at Carrow Road to where he has now returned after a brief loan spell at Rotherham United.
Asked specifically about bringing the prolific Becchio back to Elland Road, Redfearn admitted: “He’s somebody I fancied.
“Obviously he is well known at Leeds United and he has scored a lot of goals for Leeds United.
“He knows this division and he would be one for me that would give us good competition, definitely.
“The president is still away (in Miami). He’s not back until Friday but obviously I have had dialogue and conversation with him.
“I think things will really start to take off when he gets back.”
United have been hit with a Football League transfer embargo but can still sign players without a fee while the likes of Becchio could be brought in on loan.
Redfearn was also asked about the possibility of bringing another former striking ace back to Elland Road in Jermaine Beckford who is currently on loan at Preston North End from Saturday’s opponents Bolton.
Quizzed about Beckford, Redfearn replied: “The ideal scenario is that we get two or three signings that just freshens things up a little bit and gives us a little bit of competition.
“We just lack a little bit of balance in terms of experience at this level.
“I don’t really want to go in talking about certain players but the fact of the matter is we need some experience.
“We need two or three players to stiffen us up a little.”
United are also thought to be chasing Palermo’s Ivory Coast centre-back Sol Bamba, Sassuolo’s Italian striker Leonardo Pavoletti and Inter Milan’s Slovenian centre-midfielder Rene Krhin.
The Whites head to Bolton on Saturday sat fifth-bottom in the Championship with Redfearn’s men just one point above the dropzone following a five game Championship winless streak.
On the back of last weekend’s 1-0 FA Cup third round exit at Sunderland, United have won just one of their last eight games in all competitions and the Whites have not scored in five hours of football.