The Republican bench for vice presidential candidates is deeper than for presidential candidates this election year, Sen. Lindsey GrahamLindsey GrahamOvernight Finance: McConnell offers 'clean' funding bill | Dems pan proposal | Flint aid, internet measure not included | More heat for Wells Fargo | New concerns on investor visas Senators buck spending bill over Export-Import Bank Pelosi pans latest GOP stopgap spending offer 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.
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."