The owners of the Postings shopping precinct in Kirkcaldy town centre are engaged in talks with Fife Council following the decision by Tesco to leave the site on April 4.
Threadneedle Investment would not be drawn on details about its future plans - or rumoured pre-planning applications for the site.
A spokesman said: “We are looking at all options and are working closely with Fife Council to move things forward.”
The local authority put on hold £95,000 improvement works to the steps to the Postings at Bell Inn Wynd, which were due to start last month.
Councillor David Ross, Fife Council’s leader said: “Council officers are in ongoing discussions with Threadneedle regarding the future of the Postings.
“No decision has been taken on the Postings steps as yet.”