The 29-year-old has recently been linked with a move away from Hearts. The speculation has been fanned by the decision of McAvoy and Technical Director Steven Naismith to cut the player from the European squad ahead of the Conference League play-off tie's first leg at Tynecastle on Thursday night.
Peter Haring has also been left out but is absent due to injury after rolling his ankle.
“We have a squad to pick from and Jorge has been unfortunate but that is competition and it's great to have that,” explained McAvoy.
Asked specifically about Grant’s future, McAvoy denied the decision meant the player’s time at the club was drawing to a close.
“He is still part of the squad, we've told him that,” he said. “We've just got to make our decisions in terms of the legal requirements (for a 25-man squad) you have got. We've sat as a group and worked through it.”
McAvoy admitted Hearts, who enjoyed a memorable win over Rosenborg at Tynecastle to go through last week, will have to reach new heights against PAOK, who began their Greek Super League season with a 3-0 win over Asteras Tripolis on Sunday.
“There's no doubt we need to go up a level again, we will need to lift the level a wee bit more,” he said. "I believe we are capable of doing that.”