The 31-year-old striker had a frustrating spell in China following his move from Al Ain to Shanghai SIPG in 2015 and was relegated to the club's junior side at a point.
That decision by coach Sven-Goran Eriksson prompted the striker to make a loan move back to the UAE, joining Al Ahli until end of the season.
However, the former Sunderland star was denied an extension following the expiration of his SIPG contract. His counsel has met with the top hierarchy of Bursaspor and is expected to earn €30,000 every week, according to reports.
Gyan was previously approached by Turkish giants Besiktas, who could not meet his demands. He also had a failed medical last season at English Championship side Reading FC, which the player denied though.
He is expected to arrive in Turkey next week to have his medical and complete the deal.
The Black Star scored seven goals in 20 appearances for SIPG across two seasons as well as six goals in 14 appearances for Ahli.