Englishman Hatton has played in three Ryder Cups and partnered Spaniard Rahm to win two matches in Rome last year, helping Europe reclaim the trophy.
The world number 15 joined the Saudi Arabia-backed LIV circuit last month, signing up to be part of an expansion team captained by Masters champion Rahm, but the move could derail his hopes of playing in the biennial team competition again.
Ryder Cup stalwarts Sergio Garcia, Ian Poulter and Lee Westwood were ineligible this year after joining LIV and resigning from the Europe-based DP World Tour.
While Rahm's switch prompted Rory McIlroy to say the DP World Tour must change its eligibility rules, Hatton said the Spaniard was a special case.
"Jon's in a different position to me - you can't really imagine the European Ryder Cup team without Jon," Hatton told London's Daily Telegraph.
"It's nice to hear your team-mates say nice things about you and your contribution but when you talk about the Ryder Cup 'certainties' or whatever, I don't feel that I'm up there in that bracket with those guys.
"I'm sorry, I'm just not and can't rely on my reputation," added Hatton, who won six times on the European tour and picked up his sole win on the PGA Tour in 2020.
The next Ryder Cup takes place at Bethpage Black in Farmingdale, New York.
Talks over a potential merger between LIV Golf and the PGA Tour have been ongoing since a framework agreement last June, although a December 31 date to rubber-stamp the deal was missed.
