Athletic Director Dave O'Brien presented the offer during an afternoon on-campus meeting, prompted partly by the news Wednesday that USC Athletic Director Mike Garrett had asked permission to interview Greenberg.
Greenberg would not say whether he is interested in the USC job held by interim Coach Charlie Parker.
"I really don't want to get into that," Greenberg said. "I get paid by Long Beach State to win games."
Greenberg, 38, has three years remaining on his contract and officials said O'Brien is willing to extend it another year.