Elfsborg are interested in taking Cibicki on a permanent basis after signing him from Leeds on loan for the start of the Swedish season, which began at the end of March.
Cibicki has scored four times in 11 league appearances in Sweden and is on the list of players who United intend to remove from their wage bill before the start of the next English term.
Leeds handed a four-year contract to Cibicki when he signed from Malmo in 2017 but he has been surplus to requirements for almost 18 months.
Elfsborg director Stefan Andreasen confirmed to Swedish media that he wanted to strike a deal to secure the forward full-time, saying: “There were three parties who found a good solution last time and we will see if there is a possibility once again. It’s clear that we would like to see Pawel remain in Elfsborg.”
Cibicki was part of the raft of signings made by Leeds in Andrea Radrizzani’s first transfer window as owner but many of those players are no longer part of the plans at Elland Road and United will attempt to free up money by moving them on.
Turkish club Trabzonspor plan to keep Caleb Ekuban after his successful year-long loan with and despite failing to convince Getafe to buy him for £6m, midfielder Samuel Saiz is understood to have attracted at least one approach from another Spanish top-flight team.
Laurens De Bock, Eunan O’Kane and Tom Pearce, who all spent time away from Elland Road on loan this season, are others who Leeds will listen to offers for.