The Hammers are preparing for a return to Premier League action this weekend after securing a 3-1 comeback victory over Backa Topola in their opening Europa League group-stage game on Thursday night.
Bowen missed the contest at the London Stadium due to illness, while Cresswell was forced off at half time with a hamstring injury.
Providing an update on the West Ham duo ahead of their visit to Anfield, Moyes said: "Jarrod Bowen has had a virus and we'll need to see how he is for the weekend. The others, I think we seem okay.
"Aaron Cresswell had to come off on Thursday night with a bit of a hamstring problem, so we'll check him out, but apart from that we're probably about okay."
Bowen has been one of West Ham's standout performers so far this season, scoring three goals and providing one assist in five Premier League appearances to help the Hammers climb into the top six.
Cresswell, meanwhile, has had to play second fiddle behind fellow let-back Emerson Palmieri and made his first appearance of the season in Thursday's win over Backa Topola.
Summer signing Edson Alvarez was forced to miss West Ham's Europa League opener due to suspension, but the Hammers will be boosted by the midfielder's return against Liverpool.
Fellow new recruits James Ward-Prowse and Mohammed Kudus are also available for selection and will be looking to continue their bright starts to the campaign since joining from Southampton and Ajax respectively.
Ward-Prowse has score two goals and provided five assists in five games for West Ham so far this season, and the dead-ball specialist set up Kudus for his first goal for the club on his full debut on Thursday.
"I'm pleased [Kudus] has made a big impact for us already," said Moyes "He's still getting used to us and we're getting used to him, but he made a big contribution last night for us.
"James has settled in brilliantly well. We felt he had a good chance of settling in quickly due to his Premier League experience, but bringing him in was always a chance to see if he could bring goals and assist to us.
"He's a Mark Noble-type player for us in many ways, in terms of what he brings to the team."
West Ham are seeking to win their third successive Premier League away game on Sunday, but they head to Liverpool having won just one of their last 50 league visits to Anfield - a 3-0 victory in August 2015.