The Foxes had a bid for the 26-year-old midfielder turned down on Tuesday but have now returned with an improved offer, which matches Wigan's valuation of the player.
Nigel Pearson has turned to McArthur after becoming frustrated in his pursuit of former Real Madrid and Inter Milan midfielder Esteban Cambiasso.
McArthur, who joined Wigan from Scottish side Hamilton in 2010, has played in all four of the Latics' Championship matches this season, scoring one goal.
He was part of the Athletic side who won the FA Cup in 2013 under Roberto Martinez.
Leicester manager Pearson spoke earlier this week about his desire not to be 'held to ransom' as the transfer deadline approaches.
"We've had our fingers burnt in the past with doing deals late in the window,” Pearson said.
“I recognise we need one or two extra players but I'm certainly not going to be held to ransom.
“My advice to the football club is if we can't get the people we want, I don't want to pad it out with players who are not the right fit or not good enough.
"There are more hoops to jump through this year but I'm not involved at that level. I'm very happy with the players here - the numbers are the issue.
“We have an interest in a midfield player and if we can add another defender and a forward, I'd be happy."