The former Rennes ace has been linked with a close-season move despite only joining last August following a £13million switch.
Russian outfit Zenit St Petersburg are thought to be interested and agent Fabien Pivateau claims at least one bid has been made.
Pivateau has confirmed Gyan will be returning to pre-season before he holds crunch talks with manager Steve Bruce over the striker's future.
"I can't say if he is staying or not," explained Pivateau in The Sun. "As far as I know one club has tabled an offer.
"He is returning to the club for pre-season and we will sit down with the coach to talk about it."