However, Fehrnstrom clarified "the governor hasn't made a decision. It will only happen after he makes a decision."
Presidential candidates traditionally reveal their picks a bit later in the campaign season, the AP wrote.
But many Republicans predict Romney will announce his running mate well before the Republican convention in Tampa in late August, Reuters reported.
The news agency said Romney is mulling over three top contenders: Ohio Senator Rob Portman, former Minnesota Governor Tim Pawlenty and Louisiana Governor Bobby Jindal.
On Monday, Jindal helped Romney at a fundraiser in Louisiana as he has in recent weeks.
Reuters reported those also under consideration include Wisconsin Rep. Paul Ryan and Florida Sen. Marco Rubio.