Gronkowski, who suffered the injury in Sunday's wild 27-26 win over the Cleveland Browns, will undergo an MRI on Monday, according to the source.
FoxSports earlier reported that the Patriots believe it is a torn ACL.
New England announced during the game that Gronkowski suffered an injury to his right leg. Patriots coach Bill Belichick revealed after the game that Gronkowski was taken to a hospital.
"Rob was taken to the hospital for observation and evaluation on his injury," Belichick said. "That's all I have on it."
Gronkowski suffered the injury in the third quarter after hauling in a pass up the seam from Tom Brady. The two-time Pro Bowler took a direct hit to his right knee by Browns safety T.J. Ward and fell to the ground, clearly in pain.
"It was a decision I made just to make a tackle on a big man and unfortunately he got hurt, but if I would've hit up high, there's a chance I would get fined and all that other stuff. I'm just being safe," Ward said.
Medical personnel immediately came to Gronkowski's side, and he was eventually taken off the field on a cart. The burly tight end was unable to put weight on his right leg as he moved from the ground to the cart.
"My intention is never to hurt anyone," said Ward. "That's not what this game is about. That's not how I play, I hate to see guys go down with any type of injury and I just wanted him to know, whether he accepted it or not, it wasn't an intentional hit to injure him. But we have to play this game, we have to play it the way that they force us to, and unfortunately, we incurred an injury for him."
The 24-year-old Gronkowski missed the first six games of this season while recovering from offseason back and forearm surgeries. He has starred in the six games since, catching 37 passes for 560 yards and four touchdowns.
Signed to a lucrative contract extension during the 2012 offseason, Gronkowski has become a centerpiece of the Patriots. He set an NFL record for tight ends with 17 receiving touchdowns during the 2011 regular season.
ESPNBoston.com Patriots reporters Mike Reiss and Field Yates contributed to this report.