Surrey have made an approach for Durham all-rounder Scott Borthwick and opener Mark Stoneman, BBC Newcastle reports.
The pair are both out of contract at the Riverside at the end of the 2016 season, and Surrey have issued a 28-day notice to speak with the players.
Stoneman, 29, and Borthwick, 26, both topped 1,000 first-class runs in 2015 and Borthwick has been tipped for an England Test recall this summer.
It is understood both players have been offered new contracts by Durham.
Speaking to the BBC earlier in June, Borthwick said there were "question marks" over a new deal.
"The wickets here don't really help the leggies," he said. "There's been talk of me moving counties, going to where it does spin, but I've enjoyed my batting up here.
"Durham have been loyal to me, giving me the chance up the order and I would love to stay."
BBC Newcastle's Martin Emmerson
"Sunderland-born Scott Borthwick is one of the best batsmen in the country and is on the fringes of a recall to the England Test side having played once for his country in an Ashes Test in Sydney in January 2014.
"Many believe the spin-friendly surface of The Oval would suit his bowling style as well.
"He's taken nearly 300 wickets in all formats too, but Division One cricket would also be a priority for a player with international hopes.
"Mark Stoneman, from Newcastle, is one of the best openers in the country, and he is also Durham's limited-overs captain.
"The club is also waiting to see what the central contract situation is for Mark Wood because he has missed the start of the summer with England due to two ankle operations."