Dave Whelan expects to hear next week whether Roberto Martínez wishes to remain at Wigan Athletic and believes his manager should stay for the crucial challenge of returning to the Premier League at the first attempt.

Wigan became the first club to win the FA Cup and suffer relegation in the same season when they fell to a 4-1 defeat at Arsenal on Tuesday. Eight years in the top flight and the largesse of their multi-millionaire chairman have left the club in a stable financial position ahead of the drop into the Championship, but they now face the break-up of their Cup winning team and the potential departure of the manager.

Martínez was among the leading candidates for the Everton job before the FA Cup triumph over Manchester City, though no approach has been made from Goodison Park so far. Everton's chairman, Bill Kenwright, has confirmed the club will take their time to consider a successor to Manchester United-bound David Moyes and has several options, with Celtic's Neil Lennon, Vítor Pereira of Porto and Malky Mackay of Cardiff also in the frame.

The Wigan manager's future, and Whelan's championing of Martínez, has become a regular end-of-season issue at the DW Stadium. The Spaniard rejected Aston Villa and signed a three-year contract extension with the Latics in 2011 and was approached by Liverpool before their appointment of Brendan Rodgers last summer. Whelan does not expect relegation to deter would-be suitors this year.

"We'll have a meeting after the final match and he's so honest he will tell me then whether he is staying or going," said the Wigan chairman. "He has had numerous offers. There's clubs bigger than Everton looking at Roberto every season because he's a quality manager. We have a partnership, we have complete trust in each other, that's how we operate. Of course we would love him to stay but what he decides, I will accept."

Whelan admitted it is crucial for Wigan's financial health to win immediate promotion back to the Premier League as "the parachute payment is the biggest [in the first season after relegation] and we should have the same core of players." The future of key players is already in doubt, however, with the Republic of Ireland midfielder James McCarthy coveted by several leading clubs, Arouna Koné impressing in his debut season in English football and Callum McManaman rising to prominence during the FA Cup run. Antolín Alcaraz, the Paraguay defender whose injury problems had a major impact on Wigan's league campaign, and the established left-back Maynor Figueroa are both out of contract at the end of the season.

"We've got one ambition now and that is to come straight back up next season," the Wigan chairman added. "We'll look to come back within that first season, it's so important. I hope Roberto waits and has another one or two years with us. When the days dawns – and it will – when he says: 'Chairman, I want to go to this or that club,' I will release him immediately. He is aware of that, and if that time is now, so be it. But somehow I don't think it will be. I'm just hoping Roberto waits and has another one or two years with us, because he will eventually go to a top European club."

Perversely, and unlike Everton, Wigan will have European football with which to tempt Martínez next season, having qualified for the Europa League through the FA Cup. "We are going to have to have more players," said Whelan. "Take into account the Community Shield against Manchester United and we could end up playing 60 games. We will need a bigger squad."

The Wigan chairman also said it was impossible to choose between lifting the FA Cup at Wembley or remaining in the Premier League for a ninth season in succession. He said: "The FA Cup is monumental and historic but to be in the Premier League is so important commercially and financially. What made the difference this season is that Lady Luck deserted us. We had the most horrendous luck with injuries – sometimes eight first-choice players out with injury. We accept that overall we were not quite good enough but we also feel hard-done-by."