Koumas has fallen out of favour at the DW Stadium, making only eight Premier League appearances this season, and has been linked with a return to West Brom. The 30-year-old left the Hawthorns for Wigan for a fee of £5.3m in 2007.
"We have had clear interest from two teams, he needs to play games. It would be a good opportunity for Jason to regain match fitness," said Martinez.
"He has been in a mode over the last three years where he hasn't played enough football."
A permanent deal cannot be arranged until the summer as the transfer window has now closed but loans to Football League clubs are still allowed. Koumas had a spell on loan at Cardiff from West Brom during the 2005/2006 campaign.
Source: BBC Sport
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Source: BBC Sport