Marques, who is nearing the end of a one-year deal at Elland Road and, at the age of 30, would be free to leave this summer if the two parties are unable to agree an extension to his contract.
A statement released by the club confirmed that they hope to re-open talks at the end of the League One season, but it seems likely that United's plan of retaining Marques will depend on the outcome of their bid to return to the Coca-Cola Championship next month.
Watford and Crystal Palace have been linked with close-season bids for Marques, but Leeds are reluctant to lose the experienced centre-back without a fight after a year in which he has stood out as one of their most consistent and influential players.
United's statement read: "The club have agreed with the player and his representatives that it is in both parties' best interests to suspend discussions until the end of the season.
"The removal of discussions from the agenda will allow Rui to concentrate on making a positive contribution as the club look towards gaining promotion to the Championship.
"The club had hoped that Rui's future would have been secured by now. However, the respective differences in valuation, influenced by alleged interest from clubs already in the Championship, have seen us not achieve our aim.
"We still remain positive that we will be able to retain the player's services when we know what division we are going to be playing in."
Marques was promised a new deal by Dennis Wise in January, but was advised by the former boss to delay any agreement until the end of the League One campaign to maximise his earning potential if United returned to the Championship.
Gary McAllister, however, urged Leeds to initiate contract talks with Marques shortly after his appointment as manager, but initial negotiations have not reached a positive conclusion.
Marques currently has a hamstring strain and has missed United's last two games.