The surgery will be performed in Florida by Dr. James Andrews, according to the source.
Gronkowski tore both his ACL and MCL in a game against the Cleveland Browns on Dec. 8. Surgery on the ACL was delayed to allow time for the MCL to heal.
The surgery gives Gronkowski a 6½-month window until the projected start of 2014 training camp in late July.
Similar to 2013, Gronkowski's status at the start of training camp –- and if he opens the season on the physically unable to perform list (which seems likely) -- will be closely monitored.
Gronkowski has spent parts of the past month around his teammates. When the Patriots watched the movie "Lone Survivor" as a team on Dec. 20, prior to their game against the Baltimore Ravens, Gronkowski was present as teammates pushed him into a nearby theater in a wheelchair.
The Boston Herald earlier reported Gronkowski's plans to have the ACL surgery this week.