The 2009 world champion, 34, has been vying with Kevin Magnussen, 22, for the right to partner Fernando Alonso.
The team plan to make their decision public at a news conference at their Surrey factory on Thursday morning.
Spaniard Alonso, a double world champion, has returned to McLaren after five seasons with Ferrari.
McLaren chairman Ron Dennis said at the final race of 2014 that a choice between Button and Magnussen would be made on a "clinical and emotionless analysis of the options".
Button, who made his F1 debut in 2000, said at an awards ceremony on Sunday: "It's a strange situation but sometimes in life you find yourself in these situations. You just have to deal with it."
If the Englishman, who finished eighth this season, misses out on a McLaren drive for 2015, his F1 career could be over.
Rival teams have already confirmed their driver line-ups for next year.
Alonso's future was decided some weeks ago but Dennis has vacillated over who to choose as his team-mate.
He had to weigh up the pros and cons of Button's experience and greater performance in 2014 - he scored more than twice as many points as Magnussen - against the Dane's youth and potential.
Financial considerations may also be part of the decision.
Button was earning a salary of £12m in 2014, while Magnussen, in his debut season, was on about £500,000.
The Dane finished 11th in the standings, having taken second place in the season-opening Australian Grand Prix in Melbourne.
If Button is axed by McLaren, he has an option to move to the FIA World Endurance Championship, a path followed by his friend Mark Webber when he retired from F1 at the end of 2013.
Button, who began his F1 career at Williams, also has a passion for triathlons and could turn his focus in that direction.
McLaren's capture of Alonso was sealed weeks before the end of the 2014 season, but the team were waiting to make a decision on their second driver before announcing the complete line-up.
Alonso left Ferrari after their worst season for 21 years convinced him they were not capable of winning the world championship in the foreseeable future.
The Spaniard believes he has a better chance of success - and a third world title - with McLaren.
The team have had a difficult two seasons but their new engine partnership with Honda and a team restructure, which included the signing of key personnel, helped persuade Alonso to join.
Alonso endured a difficult single season with McLaren in 2007, leaving just one year into a three-year contract.
But his need for a more competitive car and McLaren's desire to sign an A-list driver convinced the two parties to work together again.
Alonso is reputed to have signed a deal worth $40m (£25.5m) a year, which would make him the best-paid driver on the grid.
The contract is believed to be for two years with an option for one more, but Alonso will almost certainly be able to leave at the end of 2015 if McLaren's performance is not up to expectations next season.
Jenson Button's Formula 1 future will become clear on Thursday when McLaren announce their driver line-up for 2015 after weeks of wrangling.