Stokes was on target in a 2-1 defeat to Borussia Monchengladbach in a pre-season friendly at Parkhead.
And the Irishman showed signs he could be the one to deliver the goals for the Hoops after striker Hooper sealed a move to Norwich.
Parker said: "It's up to him. He's there at the moment.
"Whether we bring someone in or not, I don't know.
"We've got a few options so we will see what happens. It's up to Stokes to stake a claim."