The 41-year-old is currently in charge of the League One side but is wanted at the King Power Stadium to work with boss Craig Shakespeare.
The pair are good friends having worked together as coaches at West Bromwich Albion's academy in the past and it now looks like a reunion is set to take place this summer.
Appleton has enjoyed a successful spell with the U's as he guided the club to promotion from League Two in 2015-16 and they then finished eighth in the third tier last term - just four points off a play-off place.
But the opportunity to work with the Foxes, in a deal which will reportedly double his Kassam Stadium wages, looks like proving too lucrative to turn down for Appleton.
It's being reported that Foxes and Oxford officials have been thrashing out an agreement for compensation over the weekend and an announcement is thought to be due very soon.
An indicator of Appleton's decision was reflected by Patrick Thistle defender Liam Lindsay opting against a move to Oxford when it appeared to be a done deal.