"I haven't talked to the Cowboys yet," Surtain said, per Mike Fisher of 105.3 The Fan. "I'm still in the process of talking to teams so I haven't talked to them yet."
Dallas owns the 10th overall pick in the draft, and it's still in the market to upgrade its secondary before next season, so Surtain has been rumored as a potential target in the first round.
The 20-year-old Florida native is coming off a standout season with the Crimson Tide. He recorded 37 total tackles, nine passes defended, an interception and a touchdown across 13 appearances to earn 2020 SEC Defensive Player of the Year honors.
Although he hasn't been in direct contact with the Cowboys front office, he explained on the Michael Irvin Podcast that he's talked to former Bama teammate and current Dallas corner Trevon Diggs, who's apparently been relaying some information.
"I talk to Diggs a lot of the time," Surtain said last week, via Fisher. "He's been telling me they have a lot of interest in me."
He added: "It would be really cool to reunite. I think it would be like college with me and him on both sides of the field. It would be an awesome feeling."
Surtain is one of the top cornerback prospects in the 2021 class alongside Virginia Tech's Caleb Farley, South Carolina's Jaycee Horn and Northwestern's Greg Newsome II.
Any of those corners would be a helpful addition to a Dallas defense that ranked 23rd in yards allowed and 28th in points allowed during the 2020 season.
The draft kicks off April 29, giving the Cowboys plenty of time to make contact with Surtain if he's one of their preferred targets at No. 10.