The 33-year-old is currently a free agent after leaving Steve Cooper's Tricky Trees following the expiration of his short-term contract at the City Ground in June.
Ayew featured 13 times for Forest as they managed to secure Premier League safety, however only one of those appearances was from the start, and the attacker did not do enough to earn a future in the East Midlands.
The 83-time Ghana international is most known in England for his spells at Swansea City and West Ham United, where he racked up 141 and 50 appearances respectively.
According to TEAMtalk, Sheffield United are considering a move for Ayew in the coming days, with Paul Heckingbottom hoping to improve the Blades' attack despite the window being shut.
It is understood that the Premier League newcomers are not alone in their fondness of the attacker, with the player having also attracted interest from sides in Saudi Arabia and Turkey since leaving Forest at the conclusion of the 2022-23 term.
Due to Ayew's status as a free agent, the Blades are still able to bring the Ghanaian to Bramall Lane even though the transfer window slammed shut well over a week ago.
Much has been made of United's offensive issues during the start of the top-flight season, with Benie Traore and Will Osula starting all three of their opening matches.
Successive defeats against Crystal Palace, Forest and Manchester City were characterised by a lack of attacking threat from a relatively inexperienced forward line, however the Blades were able to secure the permanent signing of Cameron Archer from Aston Villa in the final stages of the
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