The Uruguay striker, who made a £75m move to Barcelona earlier this summer, is understood to have returned Liverpool’s training ground to collect some belongings.
But he also brought a gift with him for his friend and former team-mate, Liverpool captain Steven Gerrard.
A photo on Gerrard's Instagram account shows him and the striker smiling and holding up a signed 'Suarez 9' Barcelona shirt.
The image was accompanied by a message reading: "He is back bearing gifts. Emotional saying goodbye to the main man this morning. Best wishes to a phenomenal player."
Another image later appeared on Suarez's Twitter account, showing him in a group pose with Gerrard and Liverpool defenders Glen Johnson and Jon Flanagan.
The accompanying words read: "Today I could say goodbye to some friends, it was exciting to remember the good moments that we lived together.
"Thank you for all the joy you gave me!!!!! Great picture with @glen--johnson, @jon--flan93 and Steven Gerrard!!!!"