The Trinidad and Tobago international struggled to adapt to the Barclays Premier League after Martinez brought him from his former club Swansea 12 months ago.
Ipswich's offer for Scotland, who scored just two goals last season - only one of which was in the league - is reported to be around £750,000, which represents a loss on the £1.5million the Latics paid for the 31-year-old.
"There has been a bid accepted from Ipswich but another two Championship clubs have asked about Jason," said Martinez.
"Jason will make a decision in the next 24 hours and we will take it from there."
Martinez added: "It is a situation where it has been quite public the desire to take Jason; we are going to assess it and see what is best for Wigan and Jason.
"As it is, it is a bit in the air, but unless a deal is finalised he will be in the squad (for Saturday's Premier League opener at home to Blackpool).
"Conversations have been happening and they will continue today but they won't go any further than tomorrow.
"Tomorrow, before the big game, we need to know what Jason needs. If he is staying here he will be involved in the squad, if not we will wish him the very best because even though it was a frustrating season in the goalscoring department he played a massive part in our aim of retaining Premier League status.
"We will assess it over the next 24 hours."