McArthur's return to the Barclays Premier League had been mooted for some time but Burnley had seemed the most likely destination for the midfielder, capped 15 times by his country.
Yesterday the Wigan chairman, Dave Whelan, revealed that an offer of £5m from Leicester had been rejected, but that 26-year-old McArthur was available for sale at the right price.
Leicester duly upped the ante this morning in their pursuit of the player, tabling an offer in the region of £6.5m. However, despite the eagerness of Whelan to complete the sale, the finer points of the transaction were still being negotiated tonight.
McArthur played more than 120 Premier League games for Wigan before their relegation last season, and is expected to be a Leicester player in time for their home match against Arsenal on Sunday, seven days before Scotland face Germany in Dortmund.
If the deal is completed it will be good news for Hamilton, who wrote a sell-on clause into their agreement to sell McArthur to Wigan in 2010.
For much of the day, Wigan seemed in a hurry to say farewell to the Glaswegian. Whelan was quoted as saying: "Leicester came back in this morning and wanted a quick answer; it was all sorted out pretty quickly.
"We are disappointed to lose James but he can play in the Premier League again which is what he deserves. Leicester have been an absolute credit throughout the negotiations."