According to ESPN, Sven-Goran Eriksson's CSL side lodged a bid of $28m for the prolific Ghanaian, who was the AGL's top scorer from the 2011/12 to 2013/14.
Gyan signed a contract extension last season that keeps him contracted at the Hazza bin Zayed Stadium until 2018, but struggled for form last term.
The former Sunderland player scored 17 goals but started only 13 top-flight matches as he battled with various injury problems.
The Ghanaian skipper is currently away on holiday and Al Ain were not available for comment at the time of writing.
After finishing 2015 as the second-highest-spending league in the world after the English Premier League that trend has continued in the European off-season.
Guangzhou Evergrande have signed Brazil international midfielder Paulinho for £9.8million from Tottenham Hotspur, while former Chelsea striker Demba Ba have joined Shanghai Shenhua from Besiktas for €14million.