Webster's injury, sustained during a routine workout, could sideline him for the start of the 2014-15 season.
Wittman will be joined by Vice President of Basketball Administration Tommy Sheppard to meet with Gortat in advance of July 1, when free agency begins.
NBA teams are already making moves with the hopes of landing LeBron James or Carmelo Anthony in free agency.
LeBron James isn't necessarily leaving Miami by opting out of his contract, but he is making it clear that his goal is to win championships and nothing else.
With Miami Heat on verge of losing title for second time in four years, LeBron James and Dwyane Wade have swapped roles from 2011 NBA Finals, when James inexplicably vanished and Wade carried the load in a loss to Dallas.
After two straight blowout losses at home, the Miami Heat is one loss from an end to its title run.
Disappointed with his play the first two games, Kawhi Leonard led the Spurs to a 2-1 series lead by scoring 29 points and flustering LeBron James.
LeBron James has scored at 30 points in four of his past six Finals games against the San Antonio Spurs, all wins.
While addressing reporters before Game 2 of the NBA Finals, Commissioner Adam Silver discussed Donald Sterling and air conditioning, among other topics.
After extreme, sweltering heat at AT&T Center led to cramps for LeBron James, the San Antonio Spurs have repaired electrical problems that contributed to faulty air conditioning system in advance of Game 2.