And it never took long, Swinney said, before the Tigers' versatile linebacker Isaiah Simmons came up in those conversations.
Simmons, the All-American and Atlantic Coast Conference defensive player of the year, is considered a top-five lock when the NFL draft is held next month. He was the main attraction as representatives from all 32 NFL teams watched at the team's indoor practice facility Thursday.
Simmons, the leader of the nation's sixth best defense last year, showed off his versatility, strength and speed -- and why he figures to go very early in next month's draft.
"It's like getting three first-round draft picks in one," Swinney said.
Simmons was the leader of the country's sixth-best defense, which came a game shy of a second straight national title after a 42-25 loss to LSU in the championship game two months ago.
That did not dim Simmons' dominance in the eyes of the NFL. He lined up at several different spots last season, including safety, defensive end and linebacker, and led Clemson with 107 tackles, 16 stops behind the line of scrimmage, eight sacks and 10 pass break ups.
"He's just so unique," Swinney said. "Everybody's looking for that."
Simmons, the 6-foot-4, 229-pound junior from Olathe, Kansas, lifted weights and ran shuttle cone drills in front of representatives for all 32 NFL teams. He chose not to do the 40-yard dash, standing on his stellar time of 4.39 seconds he ran at the NFL combine a couple of weeks back.
Among Clemson's three potential first-round selections, only receiver Tee Higgins ran the 40 after missing out because of a hamstring problem before the combine.
The 6-4 Higgins, from Oak Hill, Tennessee, had a fast time of 4.54 seconds before excelling at pass-catching drills.
"I feel like I impressed more people than I thought I would," said Higgins, who had 59 catches with team highs of 1,167 yards and 13 touchdowns. "I just wanted to perform well and be me."
Terrell also stayed on the sidelines most of the sessions after running a 4.37-second time at the combine.
The 6-1, 195-pound Terrell, like Higgins, is considered a late first-round prospect.
Simmons, the first Butkus Award winner in Clemson history, spent 10 minutes or so talking with Tomlin. Simmons left the field alongside a member of the Los Angeles Chargers' organization. The Chargers have the sixth overall pick in draft.
Safety K'Von Wallace, who played next to Simmons at Clemson the past four years, has little doubt Simmons' skills will fit in today's NFL.
"He is literally built in a lab," Wallace said. "Tall, long, fast, everything you want in football player, he has it."
He expects the same in 2021 when the Tigers offensive firepower, including prospective No. 1 overall pick in quarterback Trevor Lawrence and two-time defending ACC player of the year in running back Travis Etienne could be the feature attractions.
Lawrence, the 6-6 passer who is 29-1 in his college career, will be a junior and could return to school. However, he's said he's on track to graduate Clemson in December and has thought about his NFL future.
"It's always a special day," Swinney said. "A great day for the program."