Jurgen Klopp settled on Virgil van Dijk and Dejan Lovren as his first-choice centre-back pairing towards the end of last season, but the latter is likely to miss the opening weeks of the new campaign following his World Cup exploits.
Lovren is expected to return to Melwood on August 5 after helping Croatia to the final of the World Cup, giving him just a week before Liverpool get their Premier League campaign underway at home to West Ham United.
The Liverpool Echo reports that Matip, who missed the end of last term through injury, and Gomez, who spent much of the campaign at right-back before losing his place in the side to Trent Alexander-Arnold, will be given chances in pre-season to prove that they should be first-team regulars.
Van Dijk remains Liverpool's number-one centre-back, but Klopp is open to a new partner beside him if he is impressed by either contender during pre-season.
Ragnar Klavan is once again expected to be limited to a back-up role for the 2018-19 campaign following Matip's recent return to action.