Roberto Martinez expects all his out-of-contract players, which includes Hugo Rodallega and Mohamed Diame, to leave the club.
Martinez has said he would like to keep the Colombia striker and the Senegal midfielder, who cost the club more than £7million in combined transfer fees.
But both are out of contract next month and can leave the club on Bosman free transfers.
Former England goalkeeper Chris Kirkland and Ivory Coast defender Steve Gohouri are the other players whose contracts are set to expire and they will also depart the DW Stadium.
"There are four players out of contract and I expect them all to go," Martinez said.
"The idea is to keep the same squad size as we had this season, so we need to bring four players in.
"It's important we do our recruitment before the Euros because we could miss out if we wait until after the tournament.
"We signed Antolin Alcaraz before the 2010 World Cup. That was a key moment in our history because he scored the winner against Blackburn on Monday that confirmed our eighth season in the Premier League.
"If we'd waited another month, in all honesty, I don't think we'd have been able to bring him in. So signing players is something I'd like to do quickly. Before the Euros if possible."
Martinez insisted that Rodallega leaves with his best wishes.
"I don't know if he has another club lined up but he will go with our blessing," he said of the South American.
"I can't praise him enough for his attitude. He's been very unselfish. I think everyone will look at the time he had at the club as a success.
"We have to be prepared and know we need to bring in four players as quickly as possible."
Another Wigan star linked with a move is Victor Moses, but Martinez hopes to keep the rest of his squad intact.
"I don't expect to lose anyone who is under contract," Martinez revealed.
"Obviously with the ones that are out of contract, it is something we need to accept - there are certain individual circumstances where some of the players need a new chapter or moment in their careers.
"But I don't expect to lose anyone who is under contract."