The Reds step up their preparations for the forthcoming Premier League season with two 60-minutes matches against the Serie A side.
The central defensive duo made their long-awaited returns from injury against Hertha Berlin last time out, playing the final 21 minutes of the 4-3 defeat.
Van Dijk had not played since suffering an anterior cruciate ligament injury against Everton in October 2020, while Gomez played his first minutes since damaging a tendon in his left knee while on international duty with England the following month.
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Klopp is pleased with the progress the pair are making and is confident they can get more minutes under their belts against Bologna.
"Hopefully, yes. That's how it looks in the moment," he said. "I want to make it really clear, we push nothing.
"We know exactly how they feel – how they really feel and not what they tell us because they obviously are desperate to play again.
"It looks good, this morning [it was a] normal training session. Sometimes in moments, we swap Virgil and Joe a little bit so maybe the intensity doesn't get too high, but in general it looks really good.
"How many minutes on Thursday, I don't know but there will be some minutes for sure."
Klopp may also have Alisson, Fabinho and Roberto Firmino available for selection.
All three have returned from their extended break after helping Brazil reach the Copa America final, which they lost 1-0 to Argentina.
With Liverpool launching its Premier League campaign away at Norwich City on 15 August, Klopp admits the returning trio's preparation time is far from ideal.
Nevertheless, the German said they could feature against Sinisa Mihajlovic's side, who finished 12th in Serie A last term.
"The players who play international football never have enough time; that was always like this," he said.
"You never have enough time to train and stuff like this – a week, two weeks before the season.
"[The Brazilian players] will start tomorrow with training properly with us.
"Maybe on Thursday in our two 60-minute games against Bologna, we can involve them already. I don't know yet – maybe 15, 20, 30 minutes. We have to see how they look exactly."