Olise was voted Palace's Player of the Season for the 2022-23 campaign after registering 11 assists, aiding the club's move away from trouble after the appointment of Hodgson.
Palace have already lost Wilfried Zaha this summer on a free to Galatasaray, but they are in a stronger position with Olise, given that the Frenchman has a contract which runs until 2026.
Recent reports have suggested that Chelsea have made an offer for the 21-year-old, the club where Olise spent six years as a youth player.
Manchester City - another club where Olise spent time as a youngster - are also reportedly interested, especially after the departure of Riyad Mahrez.
Hodgson has gone on record and stated that the club are in a "fight" to keep hold of the winger, as clubs are "circling" around Olise.
With Paris Saint-Germain another club said to be in for him, the lure of Champions League football and competing for major honours may tempt Olise.
Speaking in the aftermath of Palace's defeat to Sevilla in pre-season over the weekend, Hodgson said: "We have a fight on our hands to make sure he stays with us,"
"We had two outstanding wingers who were almost the best in the league - Olise on the right side and Wilf on the left. We don't have Wilf anymore. Clubs are circling around Olise."
While Palace received no fee for Zaha, they would recoup a hefty fee if Olise leaves, with Chelsea's initial bid thought to be north of £35m.
Hodgson added: "We've lost five senior players from last season and brought one in - Jefferson Lerma - he's good and we're happy to have him in, but there is still that hole of five senior players in the squad, two of whom were two of the real stars of the team."
The Eagles are seemingly willing to spend this summer though, with the transfer of Matheus Franca set to be completed this week for £26m.
However, after being linked with Demarai Gray, that move may fall through with the Everton winger now set for a move to fellow London side Fulham instead.