The Spaniard has been tipped to succeed David Moyes at Everton with the Latics' relegation from the Premier League heightening speculation that we will leave.
Whelan still hopes to hold onto Martinez after he guided the club to FA Cup glory, but the manager refused to be drawn on his plans after the 2-2 draw with Aston Villa on the final day.
The 39-year-old attended the club's open top bus parade and did confirm he will make up his mind next week.
The squad and the backroom staff boarded an open-top bus at their Christopher Park training ground before making their way into the Market Place, where thousands of supporters were waiting to welcome them.
"Over the next week we'll sit down with the chairman and we'll decide," he told Sky Sports News. "But it's just a time to be proud of the achievement of the last eight years at this level, making sure we can bounce back.
"But the football club financially and in terms of history, we're ready to break even more ground, playing in the Europa League in the group stages, and carry on making that belief and pride of Wigan very strong."
When asked about the date of his meeting with Whelan, he replied: "Well it will be a week on Monday, a week today."
Relegation from the Premier League certainly had not dampened the spirits of Latics fans as they once again revelled in the shock 1-0 victory over Manchester City nine days ago that earned Wigan the first major trophy in the club's history.
So many people crowded into the Market Place that the bus had trouble getting through, but when the squad finally did make it on to the stage, there was only one message the fans wanted to get across.
As Martinez took the microphone, he had to ask the crowd to quieten down as the chant of, 'Roberto Martinez, we want you to stay', filled the air.
The Spaniard, who first joined the club in 1995 as player and has been manager for the last four years, is the favourite to take over from David Moyes at Everton, while he has also been linked with the Malaga post in his home country.
When he was able to speak, he said to the crowd: "Let me tell you two things. One - we are the FA Cup winners. Two - we've got a special group of players and backroom staff that make Wigan Athletic proud.
"And without your support that would never happen, so we want to thank you from the heart."
There will be significant changes to the playing squad as well, but winning the FA Cup is likely to remain the pinnacle for many of them.
Club captain Gary Caldwell said: "It's incredible to see so many people come out. For the town it's a great day and the boys will remember this for the rest of their lives."