Ian Murray, the shadow Scottish secretary, confirmed he would be part of Labour’s front bench team if asked by Mr Corbyn.
He wants to see Yvette Cooper replace Ed Miliband but said if Mr Corbyn triumphed he would take on the shadow Scottish secretary role.
The backbench MP is the favourite to succeed Ed Miliband, but reports have suggested as many as eight of the politicians currently attending shadow cabinet - including leadership rivals Yvette Cooper and Liz Kendall, shadow chancellor Chris Leslie and shadow defence secretary Vernon Coaker - would refuse to serve under Mr Corbyn.
Mr Murray, the MP for Edinburgh South, said: “I think anyone who asks me to serve as shadow Scottish secretary, I’ll be accepting that because we need a Scottish voice in that shadow cabinet.
“We need to work with the new leadership.”
He said he would serve under Mr Corbyn “if I’m asked to do so”.
Mr Murray said: “I think we need a strong Scottish voice in the shadow cabinet, I think people would expect Scotland to be properly represented in that shadow cabinet and we’ve got a good job to do.”
He added that new Scottish Labour leader Kezia Dugdale is “doing a tremendous job in Scotland turning the Labour Party around, talking about our values again, getting stuck into the big issues that people care about”.
Mr Murray said: “We want to make sure that that’s represented in the shadow cabinet so they can work in partnership for the benefit of Labour values and Labour voters.”
The contest has been plagued by internal rows over Labour’s direction and concerns that non-party supporters have tried to influence the outcome.