We understand that as well as the Spireites, fellow National League side FC Halifax Town, Ayr United of the Scottish Championship and an unnamed third division club in Germany have shown interest in him.
However, the 22-year-old’s preference is to stay in England.
We understand that negotiations are still ongoing with the Blues and that no deal has been fully completed yet.
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There is a chance that the move could be completed next week, but it could also rumble on further.
Gyasi still has another year left on his contract at King’s Lynn, who have just been relegated from the National League, so any transfer would command a fee.
He was loaned out to Dover Athletic during last season, where he scored five goals in 19 appearances, including against the Spireites at the Technique Stadium. He also bagged a treble against Wrexham.
He started his career coming through the ranks at Chelsea and Leicester City.
This week Chesterfield chief executive, John Croot, revealed they are ‘well down the line’ with speaking to transfer targets.
Croot told the club’s We Are Sailing podcast: “We have been speaking to a number of players and there are certainly a couple that are very close to coming to fruition. We are well down the line, we are talking to a number of players.”
The new National League season starts on August 6.
Town’s players are due back in pre-season in the first week of July, the same time that the fixtures are set to be released.
Chesterfield have announced one friendly so far, which is at home to League Two Bradford City on July 23.