United parted company with David Weir on Friday after a poor start to the season and they slumped to the bottom of the League One table after losing 3-2 to Coventry on Sunday.
Chris Morgan took charge of the team for the game at the Sixfields Stadium in Northampton.
But Robinson, who guided the Dons to a 1-0 victory at Bramall Lane on 31 August, has emerged as a frontrunner for the role.
Nigel Clough, sacked as Derby manager after defeat to east midlands rivals Nottingham Forest on 28 September, has also been linked to the vacancy.
Don't do it Karl, They have foreign owners, if you don't provide instant success they'll ship you out which will leave a black mark on your CV, you've done a terrific job with the MK Dons so you should use Sheffield United's interest as away to get the MK chairman to give you some extra funds in January to bring in that extra bit of quality for a promotion push.- dannyjohnson