The team, who are starting a new partnership with Honda and have yet to announce a title sponsor, invited reporters to their Woking headquarters for "an important and exclusive media event".
No details were given but the move was widely interpreted as evidence a driver decision had finally been reached after a board meeting last week ended without news.
Button's future has been the big question for months, with the 34-year-old Briton out of contract and McLaren the only team yet to name their drivers.
One is sure to be Spain's double world champion Alonso, already replaced at Ferrari by four times title-holder Sebastian Vettel, whose return has yet to be confirmed officially by McLaren despite being an open secret.
Spanish media, who last month quoted the King of Spain as saying Alonso had told him he was joining McLaren, had no doubt the announcement was imminent.
Alonso spent one turbulent season at McLaren in 2007 before leaving following a breakdown in relations with then principal Ron Dennis, who is now overall group head.
The Spaniard's team mate has looked a straight choice between Button, the sport's most experienced current driver, and Danish youngster Kevin Magnussen, who formed this year's pairing.
The Daily Mail newspaper, citing "an impeccably-placed source" within McLaren, said Button had been offered a new contract.
'CLINICAL ANALYSIS'
If confirmed, it will be a bitter blow for 22-year-old rookie Magnussen, whose future remains unclear despite having youth and promise on his side.
Dennis said last month that the choice would be made on a "clinical and emotionless analysis of the options".
But there has been plenty of emotion from fans of both drivers, with Button sparking a lively reaction when he addressed the subject at Sunday's Autosport Awards in London.
"Do any of you think I should be racing in F1 next year?" the Briton asked the audience, to raucous cheers of support, before adding it was a "strange situation" to be in.
"I've got a new Japanese (mobile) number so that might be why I haven't heard anything," joked the winner of 15 races, whose last victory in Brazil 2012 also remains the team's last.
"If it was my first year in F1 it would be a lot more difficult, but I've had an amazing career in Formula One."
(Editing by Ken Ferris/John O'Brien)
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