"I'd love to be part of the Wigan squad in the Premier League, but the deal has to be right and I've got to do what is best for myself and my family because this is a crucial decision in my life.
"I've the most important years of my career ahead, but whether that is with Wigan or elsewhere I just don't know yet.
"There are other clubs interested but I want to stay with Wigan if possible.
"I'm due to talk with the club again this week and my future should be decided one way or the other by Sunday."
Jarrett, a £75,000 deadline-day signing from Bury in 2002, was not a regular in the Latics starting line-up last season after injuries blighted his campaign.
But the fact Paul Jewell has offered him a new deal at the JJB means the Wigan boss is confident Jarrett can hack it at the top level next season.
Gary Teale became the latest Latics star to agree a new deal when the winger put pen to paper on a two-year contract on Friday.
Now the Wigan boss is hoping Jarrett will follow in his tracks ahead of the squad reporting back to pre-season training on Friday week.
Jewell said: "Jason is a smashing lad who has done a good job here.
"He had a difficult time last season but came back strongly and had the best game for Wigan against Reading on the final day when we went up."
Meanwhile, Wigan say there has been no approach from Birmingham City after reports in the Midlands suggested Jimmy Bullard has emerged as a target for former Latics boss Steve Bruce.
Bruce tried to sign Bullard when he was at Peterborough – but Jewell beat him to the punch when he agreed a £275,000 deal in 2003.
Bullard is signed up for another 12 months, and Jewell added: "We are talking to Jimmy about a new deal and he will be a key player for us next season.
"He played every game for us last term and we've no intention of selling Jimmy Bullard to anybody."
Paul Mitchell, meantime, has linked up with Danny Wilson at Milton Keynes Dons.
Mitchell has agreed a two-year deal with the Dons and will join them when his Latics contract runs out on June 30.
The 24-year-old, who arrived at Wigan as a trainee, enjoyed a successful loan spell at the National Hockey Stadium last season.
Mitchell said: "Danny Wilson gave me a chance to get back playing again and the fans were also a massive incentive after the way they backed me during our fight to beat relegation last season."
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