The Foxes have been pushing to sign the 32-year-old after having an initial offer around £4m rejected last week. Talks have continued with Steve Cooper eager to bolster his attacking options after a spate of injuries.
Ayew has made 212 appearances for the Eagles, scoring 23 times and picking up 22 assists in all competitions.
The fee for the Ghanaian will be £5m with a further £3m in add-ons.
Cooper said on Thursday: 'I think we are close but we have been close before I thought the week before we were adding two attacking players but it didn’t happen in the end. That’s the way it went.
Leicester City have agreed an £8million deal with Crystal Palace for Jordan Ayew
'The top end of the pitch is an area we would like to strengthen, like we have in midfield. Every area we want to strengthen, but that might not be in this window.
'We are really keen on getting some deals over the line and we are working hard. If it happens, great, if not then we have belief in the guys who are here. That’s important.
'If we can add, and I think we will, but if we don’t get on with it and commit to our objectives.'
Ayew started on the bench in the 2-1 defeat at Brentford on Sunday, coming on for the final 20 minutes to replace Daichi Kamada.