The Republican bench for vice presidential candidates is deeper than for presidential candidates this election year, Sen. Lindsey GrahamLindsey GrahamSunday shows: Homeland Security chief hits the circuit after Manchester attack Senate panel could pass new Russia sanctions this summer Overnight Cybersecurity: Bad Russian intel may have swayed Comey's handling of Clinton probe | Apple sees spike in data requests | More subpoenas for Flynn | DOJ's plan for data warrants MORE (R-S.C.) said.

"The good news is I think we got a deeper vice presidential bench than we do presidential candidates," Graham said in an interview with South Carolina radio station WVOC published Tuesday.

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Graham listed Sen. Marco RubioMarco RubioSenate panel could pass new Russia sanctions this summer McConnell on Trump: 'We could do with a little less drama' Taking the easy layup: Why brain cancer patients depend on it MORE (R-Fla.), former Florida Gov. Jeb Bush (R), Sen. Rob PortmanRob PortmanSens submit bill to 'Hack the DHS' CBO score underlines GOP tensions on ObamaCare repeal Senate panel could pass new Russia sanctions this summer MORE (R-Ohio) and Rep. Allen West (R-Fla.) as potential candidates. 

Rubio, Bush, and Portman have endorsed Mitt Romney, the presumptive Republican presidential nominee. 

Rubio's name is perhaps the most commonly listed one on vice presidential shortlists. The argument for his candidacy is usually that he would help win over Hispanic voters and is a rising star within the GOP. Rubio has repeatedly said he would not be picked for the number two spot on the ticket. 

Portman is becoming increasingly common suggestion for a Romney vice presidential nominee. The usual arguments for his candidacy are he would help win voters in a coveted battleground state, his background as director of the Office of Budget Management during the George W. Bush administration and his experience working with Democrats. 

West's name has been floated for the presidential ticket and, unlike some of the other prospects, he's said that he would accept an offer "if it was the right fit."

"In this case, Florida and Ohio are the two great prizes. We've got Rob Portman from Ohio, a senator, who would be a really good pick," Graham added. "He's a solid guy. But you've got Rubio, Bush. You got people in Florida like Allen West, that would add to the mix."