The Latics owner claimed on Friday that Martinez had been offered the opportunity to become Kenny Dalglish's replacement at Anfield - a claim Liverpool deny - and he expects a decision in the next few days.
Whelan has made no secret of his desire to keep Martinez but if the Spaniard does go he will move quickly to replace him.
One of those in the frame could be Bruce, who is out of work after being dismissed by Sunderland in November.
Bruce had a brief spell in charge of Wigan in 2001 before returning from 2007 to 2009, and Whelan says the two of them still have a good relationship.
Dave Whelan: "Steve Bruce is someone I've always got on with.
"I never sacked him. He left for Sunderland but we've remained on good terms.
"I've not spoken to anyone yet and I don't need to because there are one or two excellent managers around at the moment who aren't in work."