Newly-appointed boss Enzo Maresca is leading a rebuild at Leicester following the club's recent relegation to the Championship.
The Foxes are expected to strengthen in a number of areas, including the centre of defence, where they have been weakened by the departures of Caglar Soyuncu and Daniel Amartey.
Jonny Evans is also out of contract at the end of the week, and he could be the next player to leave if the two parties are unable to reach an agreement over a new deal.
A recent report revealed that Leicester were pursuing a deal for Coady, who has returned to Wolves following a loan spell with Everton.
Coady made 24 appearances Premier League appearances last term, but Everton decided against taking up the option to sign him on a permanent transfer.
According to journalist John Percy, Leicester are on the verge of signing Coady after reaching an agreement with Wolves.
The Midlands club rejected an initial bid from the Foxes, but the two clubs have now agreed upon a £7.5m fee, which will rise to £8.5m if Leicester win promotion to the Premier League.
The England international will undergo a medical on Thursday, before he can be officially announced as a Leicester player.
Coady, who joined Wolves in 2015, will leave Molineux after making 317 competitive appearances, contributing seven goals and seven assists.
The England international was part of the Wolves side that won promotion to the Premier League during the 2017-18 campaign, and he will be looking to replicate that feat with Leicester.
The Foxes are also said to be pursuing a deal for Tottenham Hotspur midfielder Harry Winks, who spent last season on loan at Sampdoria.
Leicester will begin their promotion bid on August 6 when they welcome Coventry City to the King Power Stadium for their Championship opener.