Previously, Murphy had indicated his desire to move on to bigger things and play Championship football, so he was considered for the Republic of Ireland squad on a regular basis.
However it seems the fans favourite may see his future at United after a great start to the season.
"I'd like to stay here if we got promoted. I'd love to stay," he told BBC Radio Humberside.
"I think we'd do well [if we went back up] because we've learnt lessons from last season.
"Personally, I'll make a decision at the end of the season. I just want to concentrate on my football now. It's only early days, but if we get promoted I've got a lot to think about."