The Reds travel to Vicarage Road to face the Hornets a week on Saturday in the opening game of the 2017-18 campaign.
But they will seemingly be without Clyne, with the England international sidelined by a hamstring injury, then a back injury, that kept him out of the club's trips to Asia and Germany.
Clyne expected to miss out on Watford trip
Klopp, speaking after Liverpool's Audi Cup final defeat to Atletico Madrid on penalties on Wednesday, said of Gomez's centre-back role: "How you know, Joe can play both positions [centre-back and right-back] so it makes absolute sense that we try both positions, especially in our situation with [Nathaniel] Clyne injured."
The German revealed that Clyne is "on the way back" but has "had no pre-season so far" which means "it will not only be tight for Watford" but "pretty much impossible."
Assessing his alternative right-backs, Klopp noted that they have "three" options in Alexander-Arnold, Gomez and Jon Flanagan - adding: "All of them played the position and now we have to bring them through the next one-and-a-half weeks. Hopefully Clyney can come back after this. We have to make a decision."
The Reds boss noted that Gomez was not "as quick as he was before" when he returned from his "long injury" in "the middle of the season" but declared that he has "got it all back" and is now "in really good shape."
He called it "very important" for Liverpool that they can call upon Gomez "in both positions" in centre-back or at right-back.
While a set-back, Alexander-Arnold has thrived in pre-season and would appear the front-runner to start the opening league game. He was excellent against Bayern Munich on Tuesday as Liverpool ran out 3-0 winners.
Klopp also has a decision to make at left-back, with James Milner having underwhelmed of late and summer signing Andrew Robertson and Alberto Moreno - also impressive against Bayern although it is widely expected he will leave Liverpool this month - for competition in the position.