The Georgian international was a huge success in his spell at Maine Road before joining Ajax two seasons ago but he has failed to make an impact in the Netherlands and the Blades manager, Adrian Heath, has opened transfer talks.
"We have spoken to Ajax about the possibility of taking him on loan," Heath said. "It would be a very expensive deal but we are hoping that he would excite the crowd."
Kinkladze has also been linked with a move to Portsmouth, where the former City manager, Alan Ball, is in charge.
Aberdeen appear to have cooled their interest in Sheffield United's Brazilian striker Marcelo. The Dons, who have yet to claim their first point of the season, have lodged an pounds 800,000 bid for Marcelo.
However, although the offer remains in place, the Aberdeen manager, Ebbe Skovdahl, was unimpressed by reports he has received of Marcelo's performance in the Worthington Cup game at Preston on Tuesday and is now believed to be looking elsewhere for reinforcements.
For a player who is reportedly demanding pounds 10,000 a week to complete the move north, Skovdahl feels Marcelo could be a luxury the Dons can ill- afford in their present predicament.
The Danish coach is having difficulty recruiting the players he feels will arrest Aberdeen's current plight. So far only the former Darlington goalkeeper David Preece and the Norwegian defender Thomas Solberg have arrived at Pittodrie.
Dundee United have completed the signing of the Australian midfielder Raphael Bove. The 22-year-old became a free agent in the summer after a spell with the Dutch club Heerenveen.
Bove hopes to establish himself with United to promote his case for selection in the Australian Olympic squad for next year's Games in his native city of Sydney. He may have to wait for his debut as his new manager, Paul Sturrock, looks to build on an impressive start to the season which sees the club lie third in the table.
"Raphael plays wide right and has shown he can pass the ball well," Sturrock said. "He offers us something we lack in that area of the team."
Stan Collymore will begin his final attempt to avoid an ignominious return to Aston Villa when he resumes training with Fulham today. The on-loan striker has had a groin problem and has only three weeks left to convince the Cottagers' manager, Paul Bracewell, to make the move permanent.