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Jarrett is one of four players approaching the end of their current contracts to be offered fresh terms by the club.
The three-year deal is the longest on the table – Steve McMillan and Gary Teale having been offered two years and Gary Walsh one.
Manager Paul Jewell believes they all have a part to play in the first team squad next season, even though they were on the fringes last term.
In an exclusive interview with the Evening Post, Jarrett said: "I'm pleased to get this offer and three years is a good length of contract these days.
"My agent is meeting the club this week and hopefully everything can get sorted out soon, although these things are never easy.
"I've been here more than three years now and would love to stay longer because this is a great place to be.
"Being in the Premiership is a dream for Wigan and a dream for me, and I want to play there for Wigan.
"The best years of my career have been here and two promotions in three years have been fantastic – some players don't get that in their whole career."
Last season was a bitter-sweet one for the 25-year-old, starting with the agony of a serious ankle injury but ending with a timely return to the first team.
In between were months of uncertainty as he recovered from the injury and then endured a battle to get back into the squad.
He played a key role in the closing stages of the campaign, turning in a storming performance against Reading on the day promotion was clinched.
Jarrett said: "It was a frustrating year but the manager told me to be patient and that I would get my chance.
"I came back into the team at an important time, starting three of the last four games and coming on as a substitute in the other.
"At one stage I didn't think I would play at all in the season so it was great to be involved at the end."
Jarrett has just returned from the club holiday in Barbados, paid for by Dave Whelan as a reward for reaching the Premiership.
"The chairman really looked after us, and we hardly had to put our hands in our pockets while we there," he said.
"The hotel was lovely and we had a couple of parties at Mr Whelan's house over there – that's a beautiful place.
"A lot of the lads played golf every day but myself and Leighton Baines gave up after 12 holes on the first day!
"I preferred relaxing by the pool and taking part in some water sports.
"We're back training on July 1 and until then it's a case of getting some more rest and keeping the fitness levels up.
"I think we're coming back a bit earlier than most Premiership clubs, but the more work we can do, the better."
Meanwhile, Graham Kavanagh is in the Republic of Ireland squad for the friendly against Celtic on May 29 – a testimonial for Jackie McNamara.
And the midfielder is expected to get the call-up for the two World Cup qualifiers against Israel in Dublin on June 4 and for the visit to the Faroe Islands four days later.