Unite general secretary Len McCluskey urged Ms Maskell, the Shadow Environment Secretary, not to join other members of Mr Corbyn’s top team who quit last week.
The resignations followed the Labour leader’s decision to impose a three-line whip on Labour MPs to vote for the Government’s Brexit Bill which will give Theresa May the power to begin Britain’s departure from the European Union.
Ms Maskell, a national officer with Unite before becoming an MP in 2015, is understood to be considering whether to resign so she can vote against the Bill.
York was the most pro-Remain district in Yorkshire at last year’s referendum with 58 per cent of voters backing Britain staying in the EU.
Shadow Education Minister Tulip Siddiq and Shadow Wales Secretary Jo Stevens stood down last week and two Labour whips have also said they will not vote for the Brexit Bill.
Asked about the resignations, Mr McCluskey told The Yorkshire Post: “I know one of the Yorkshire MPs, Rachael Maskell, she is absolutely first class in terms of her role in the shadow cabinet. I know she is considering her position. I hope she doesn’t resign. She really is a top MP and a great member of the shadow cabinet.
“I think because this is such a sensitive subject of course people have to examine their conscience but there are occasions when the discipline of the party is important and you just have to accept that and continue to do your job and continue to argue for your concerns inside the tent as it were.
“I am sure that Rachael would have greater influence in the shadow cabinet than out of it, as indeed would Jo Stevens and I am sorry Jo has gone.”
Mr McCluskey said the Labour leader was “damned if he does and damned if he doesn’t” in his decision to order MPs to back the triggering of Article 50 of the Lisbon Treaty, the mechanism to begin Britain’s departure from the European Union.
“People have wanted him to give clear leadership, he has on Article 50. I think that’s trying to reflect the fact that was the decision of the British electorate.
“The most important thing for me now is what the Labour Party does in terms of pressurising the Government during the negotiations,” he said.
Under Mr McCluskey, Unite has been campaigning for continued European single market access when Britain leaves the European Union.
EU leaders have made clear free movement of people would be a condition of single market access but Mr McCluskey argued concerns about immigration could be addressed through changes to UK labour rules.
He said “greedy bosses” were abusing migrant workers, driving down wages and creating a “race to the bottom culture”.
“We should say that any employer that wants to bring migrant Labour in from Europe to work for them has to have an agreement with the relevant trade union.
“That way you would get a situation where minimum standards and conditions would be protected.
“The result would be because these greedy bosses can’t abuse migrant workers there would be a dramatic reduction in the number of migrant workers coming into the UK,” he said.
Mr McCluskey was speaking after visiting Yorkshire over the weekend as part of his campaign to be re-elected general secretary of Unite, Labour’s biggest financial backer.
He has been criticised by rival Gerard Coyne for spending too much time on Labour Party politics, in particular supporting Mr Corbyn in battles with his own MPs, rather than fighting for Unite members.
Mr McCluskey said: “He knows that 95 per cent of my time is spent on industrial matters. More importantly my shop stewards and activists and members know that.”
He accused the “hard right” of the Labour Party trying to use the Unite election as a “proxy war against Corbyn”.
Unite members will begin voting in the general secretary election in March.