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Weekend speculation in the national press had linked him with a move to Derby County, but the 32-year-old says that claim was wide of the mark.
Jackson told the Evening Post: "I've been offered another year by Wigan and had a chat with Paul about it last week.
"Everything is fine and as long as I've got a realistic chance of being in the team, I'm happy to stay.
"I know there has been interest from other clubs but I think the link with Derby has been rehashed from last season.
"I've got a while longer to consider the contract offer but I expect to be here next season."
Jackson is currently rehabilitating after suffering a torn Achilles tendon, an injury which kept him out of the last six weeks of the season.
He is now almost back to full fitness and will be ready to start pre-season training on July 1 with the rest of the squad.
"The injury is coming on great and I am back running now," said the Latics vice-captain.
"I'm going to keep in training pretty much the whole of the summer apart from when I go on holiday.
"I had my leg in a cast for five weeks, the tendon has healed very well, and the specialist is happy with it.
"I fact I was pretty confident I could have been ready in time for the play-off final at the end of the month had we got there.
"So I'll be okay to start pre-season training, and after missing the last part of the campaign, I'll be raring to go.
"It was frustrating getting the injury when I did, just at a time when I had got my place back in the team.
"I had got a kick in training the week before the game at Watford, and was a bit sore going into it.
"It then just suddenly went during the game and I knew straight away I'd done something quite serious.
"Having to watch the remainder of the games from the sidelines was frustrating, especially with the heartbreaking end we had.
"It really does make you realise how good it is to be playing and that you should appreciate it."
Jackson is the first player offered a new deal to publicly say he will be stopping.
Jason de Vos, Paul Mitchell, Mike Flynn, Gary Walsh and James Salisbury have also been offered one-year contracts and are currently mulling over the terms.
The same length offer remains open to Andy Liddell but the striker has already indicated he sees his future elsewhere – with Sheffield United the favourites to snap him up.
Source: Wigan Evening Post.