Manager Derek McInnes is desperate to bolster his options in central midfield before taking on Finnish side RoPS on Thursday.
The deadline for registering players was Friday night, but the Scottish side can add one ‘wildcard’ option before Wednesday.
McGeouch’s excellent pedigree north of the border has made him their main target.
“This European game has accelerated everything here and we know the level of our opponent is going to require the best from us,” McInnes said.
“We are light in central midfield and in an ideal world if Craig Bryson can come in that will help us but we would like another one in, although there are no guarantees.”
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McGeouch and Sunderland have a big decision to make on his future, despite the midfielder taking up the option of a further year earlier this summer.
He is currently on Wearside and has been taking part in full pre-season training.
He did make 30 appearances last season but spent long spells out of the team and missed out on the matchday squad for the play-off final.
Speaking after that game, he said: “I have a big decision to make. It’s disappointing I haven’t played as much as I’d have liked.
“I’m fit and feel good and I felt I could bring something to the team. I haven’t given up hope of making it here. I believe I can play a part in helping Sunderland be successful.”