The trio, who have a combined 25 Ryder Cup appearances between them, risked their futures as players or captains in the biennial team competition with the United States by joining the Saudi Arabia-backed LIV Golf Invitational Series.
"I hope that I still have the possibility, as I'm sure they do, too, to be a part of a few more Ryder Cup teams, but that's not going to depend on us now," Spaniard Garcia said at a news conference on Wednesday alongside Westwood and Kaymer ahead of this week's LIV event in Portland.
"We'll just keep our fingers crossed."
Westwood, who made a European record-equalling 11th Ryder Cup appearance last year at Whistling Straits and has long been regarded as a future captain, felt he deserves to remain part of the mix despite joining LIV.
"Why should it be threatened?," the Englishman said when asked if he felt it was worth it to jeopardise his Ryder Cup future to play in the lucrative LIV series.
"As long as you fulfil the criteria to be a European Tour member, then you should still have the opportunity to try and qualify for the Ryder Cup team."
Former world No.1 Kaymer of Germany, who last played a Ryder Cup in 2016, said that while he loves competing in the team format he has no regrets if his decision to join LIV costs him any future involvement in the event.
"Obviously we didn't know what the sanctions might become one day, but if you asked me if I would do the same, if I would make the same choice, absolutely, because I do believe in the whole vision that LIV Golf provides for the game of golf and for us players."
