The 32-year old winger is a free agent after playing for Pune City FC in the inaugural Indian Super League at the end of last year.
Pennant, who has previously spent time with the likes of Arsenal, Liverpool, Stoke City and Real Zaragoza, has been training with the relegation-threatened Latics and could possibly be added to Mackay's squad as he goes about rallying his side who sit second bottom in the Championship.
"Jermaine has been training with the club," he told Sky Sports News HQ.
"I have had a good conversation with him, and he is desperate to come back and prove himself in England.
"He has been playing in India, and could have gone to Thailand, but he has asked if he can come in. He has been a terrific professional the last few days, and we will see what happens."
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