The former Aberdeen defender moved to Anfield in July but has since struggled with injury during what has been a frustrating start to the season for Klopp’s side.
Brought in as cover for Trent Alexander-Arnold, Ramsay arrived on Merseyside with a back issue and did not feature in any of the club’s preseason matches, though has recently been included in a number of matchday squads.
The 19-year-old has been building up his fitness at U21 level, scoring in both the EFL Trophy and Premier League 2 already this month.
“With Calvin, we have to see,” said Klopp at Monday’s pre-match press conference.
“That makes now no sense if we have to change a lot of players to bring Calvin in for his first senior [appearance]. Coming on, yeah, for sure – these kind of things should be possible.”
Liverpool have been a further boost with Ibrahima Konate also in line to return.
A crucial figure last season, the French defender has been limited to only two appearances this time out due to a troublesome knee problem.
Like Ramsay, however, Konate has been back in recent squads and will likely play in at least some capacity at Anfield on Tuesday.
"We will see. Ibou, I think there’s a good chance that he will have a game,” said Klopp.
Liverpool can still top Champions League Group A but need to beat Napoli – one of Europe’s most dangerous sides on current form – by four goals or more.