The Republican bench for vice presidential candidates is deeper than for presidential candidates this election year, Sen. Lindsey GrahamLindsey Olin GrahamDHS chief takes heat over Trump furor Overnight Defense: GOP chair blames Dems for defense budget holdup | FDA, Pentagon to speed approval of battlefield drugs | Mattis calls North Korea situation 'sobering' Bipartisan group to introduce DACA bill in House 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 Antonio RubioOvernight Cybersecurity: Bipartisan bill aims to deter election interference | Russian hackers target Senate | House Intel panel subpoenas Bannon | DHS giving 'active defense' cyber tools to private sector Senators unveil bipartisan push to deter future election interference Puerto Rico's children need recovery funds MORE (R-Fla.), former Florida Gov. Jeb Bush (R), Sen. Rob PortmanRobert (Rob) Jones PortmanFlake's anti-Trump speech will make a lot of noise, but not much sense Top GOP candidate drops out of Ohio Senate race Overnight Tech: Regulators to look at trading in bitcoin futures | Computer chip flaws present new security problem | Zuckerberg vows to improve Facebook in 2018 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."