The Pole has been working with the Partick Thistle squad in recent weeks after being added to Alan Archibald's backroom team following the departure of Kenny Crichton at the end of the season.
O'Donnell has played in a couple of pre-season games after recovering from hip surgery but club captain Welsh has yet to turn out and didn't feature as Archibald's side lost 1-0 to Rangers at Firhill yesterday.
Szostak, who joined Thistle after a spell at Premiership rivals St Mirren, is eager to get everyone fighting fit as soon as possible as the big kick-off looms.
"Nobody wants to be in the physio room and both Stephen and Sean are just desperate to get back to playing," he told ptfc.co.uk
"Stephen started training while we were in Spain and has already taken part in games, which is brilliant to see.
"Sean is coming back from a persistent groin injury but is making great progress with his rehab and is very focused on getting back to playing football.
"I see all the injured boys every morning to see how they're getting on. They each have a plan laid out for them so, depending on how their recovery is going, that might need updated.
"After each training session we'll assess the guys that have trained.
"If they have any complaints, maybe a bit of stiffness or a wee knock, I might take the decision to pull them out of training the next day so as not to exacerbate anything."