Hull have held a long-term interest in Nikolic, 28, and tried to sign him in the summer, but their ongoing takeover talks held up any move and he ended up staying at Legia Warsaw.
The Hungary international has scored 13 goals in 28 appearances in all competitions for Legia this season, but the Polish club have been eliminated from the Champions League and Europe altogether so they are ready to sanction his sale.
Hull have expressed an interest in signing Nikolic when the transfer window reopens next month as Mike Phelan is desperate to bolster his attacking options after losing Will Keane to injury for the rest of the season.
Phelan has made striking reinforcements his top priority in January as he looks to add goals to his side to lift them away from the Premier League's relegation zone.
However, sources have told ESPN FC that Hull are poised to be beaten by Chicago Fire in the race to sign Nikolic.
The MLS side are busy preparing to improve their squad for next season after a disappointing campaign and are hopeful of luring Nikolic to the United States after opening talks with Legia.