The pair, who are both suffering with a stress fracture of the foot, played no part during Pool’s opening pre-season friendly at Southport on Saturday.
After the 2-0 win, head coach Michael Appleton told The Gazette Stewart and Beesley are facing six to eight weeks on the sidelines, which would rule them both out of the season opener against Reading on July 30.
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Beesley, who was seen wearing a protective boot at Haig Avenue, suffered the blow during the first few days of pre-season training.
“He’s got an issue with the foot, a stress fracture,” Appleton said.
“He’s going to be in the boot for four weeks I think, so that might be a six to eight-weeker depending on how quickly it heals.
“That’s a disappointment for him and a disappointment for me because I was looking forward to seeing him, because he gives me a few options in various positions up top.
“You could tell he was a bit gutted when the injury came about.”
Stewart was also spotted watching from the dugout at Southport, but played no part.
Appleton has yet to see Stewart train, which also applies to Jordan Gabriel who is close to making his way back from the hamstring problem he suffered towards the back end of last season.
“Jordan and Kev, I’ve not actually seen on the grass yet and I definitely won’t see Kev for a while,” Appleton added.
“He’s similar to Jake with a stress fracture of the foot, so that will be a similar sort of timeline to Jake, albeit slightly ahead because that was done before we reported back.
“Jordan has a little bit of an issue with his hamstring, so he should be able to train mid to late next week, but I don’t think we’ll see him against Leeds (on Thursday).
“But we may see him in and around it against Rangers (July 16) as long as he comes through training okay.”