The Robins aim to complete the deal for the 22-year-old Scotland international in time for their clash with Leicester on Saturday.
Kelly, born in Milton Keynes, has scored six goals in his last nine Scottish Premier League appearances and has played over 100 times for the club since joining in 2010.
"We've agreed a fee for Liam Kelly and we now need to try and push it over the line," McInnes told the Bristol Evening Post on Thursday.
"We have to get the boy down here, do a medical and try and get international clearance pushed through.
"If he can train with us, then he can go into the squad for Saturday. Whether it can be done remains to be seen, but it is a real possibility."
Meanwhile City have confirmed they have lodged a bid for Crawley defender McFadzean.
"We've bid for him and that's as far as it's gone," McInnes told the club's official website. "It's a complicated one and we'll have to see how it pans out."
Elsewhere, the postponed Championship clash with Watford has been rearranged for Tuesday January 29, kick-off 7.45pm at Ashton Gate.
The game was originally due to be played on Boxing Day but was postponed before a ball had been kicked due to a torrential downpour, which left the Ashton Gate pitch waterlogged.