The Dutch midfielder stated over the weekend that he could not be certain of staying at Inter beyond the summer, after being linked with a move elsewhere.
Manchester United, Manchester City and Chelsea are among those to have been credited with an interest and his comments have only served to fuel speculation.
Sneijder said: "I love Inter with all my heart, but only God will decide where my future lies."
Moratti has now responded with disappointment, conceding that Sneijder's situation is causing concern.
Speaking outside his Milan offices, Moratti said: "It was sad to hear those comments."
Sneijder was brought to Inter by then manager Jose Mourinho in the summer of 2009 and, prior to the weekend, had pledged his commitment to the club.
While the 27-year-old has now been tipped to depart, Inter have been connected with a move for coach Marcelo Bielsa.
The Argentine tactician is reportedly a target to replace Leonardo, whose position has come under scrutiny after just six months at the club.
However, Moratti maintains there is no truth in the stories and has once again given his backing to Leonardo.
"There has been no contact with Bielsa, I deny everything," Moratti said. "Leonardo is an excellent coach."