FOX Sports first reported the discussions among the two teams, and Yahoo! has said there is "significant optimism that Wil Myers to San Diego gets done." Neither club has confirmed talks. The Tampa Bay Times reported a third team might be involved.
Myers, 24, struggled last season, but he hit .293/.354/.478 and was named American League Rookie of the Year in 2013.
Myers is also a very attractive piece for the Padres because he's under team control for the next five years. He will be arbitration-eligible prior to the 2017 season and won't be a free agent until after the '19 campaign.
If the Padres are able to acquire Myers, it won't be without giving up some big pieces.
Reports have not indicated who the Padres would be sending the Rays, but San Diego does have some prospects who are very close to contributing at the Major League level.
William Boor is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.