Forrest has started only 10 Scottish Premiership games after being afflicted by a number of strains, as well as illness, and he has been sidelined by a groin injury for more than two months.
Manager Neil Lennon told the Evening Times: "Jamesie will not be going away with Scotland for their game at Craven Cottage at the end of this month.
"He has had surgery on his groin and needs a bit of time to recover.
"I don't know if Nir Biton, who has been out for a few months, will be going away with Israel.
"But we are hoping they can both come back in good health for the start of our pre-season."
Lennon will begin reshaping his squad following the conclusion of their third consecutive championship win, which concluded with a 3-1 win over Dundee United on Sunday.
The match proved a farewell for Georgios Samaras, who confirmed his departure and claimed he had not been offered a new deal by chief executive Peter Lawwell.
However, Lennon is set to welcome back loan players Tom Rogic, Tony Watt, Jackson Irvine and Callum McGregor.
"They will all be coming back, Tom after we hope he has been to the World Cup with Australia," said Lennon.
"We will get the group together on June 24 and assess what we need to do."