The Mirror says Southampton are leading the chase for Garcia.
Garcia, 27, has rejected a new deal with his current contract due to expire next summer.
He pulled no punches and said sorry to the club's supporters, who were booing their team during the first half.
Pellegrino said: “My feeling is obviously that we are disappointed because we show completely different face from the other day.
“Obviously this performance surprised everybody because it is not about tactics or technical problems, we were really bad from the beginning until the end.
“When you have got those days the best thing is to try to go to the next page and prepare the game for Saturday and react to show another face and take responsibility.
“This is our job and I have to say sorry to our fans.
“You can lose games but not in this way."