Barcelona announced on 5 July that the five-time Ballon d'Or winner had agreed a new contract to commit his long-term future to the La Liga giants.
However, the 30-year-old forward is yet to sign the contract amid suggestions that his relationship with the club's board is strained.
Barcelona President Josep Maria Bartomeu has tried to play down concerns from the fans in recent weeks, saying that the club are just waiting for the right time for Messi to sign the new deal which will include a €300m (£263.5m) release clause to ward off potential suitors.
Fabregas is unaware about the state of the negotiations but has urged his former Barcelona teammate to put pen to paper on the new contract.
"I do not know, I hope so," the Chelsea star said to Marca when asked whether Messi will eventually sign the renewal. "It's him the one who has to answer this question. I have always said that there is no better home for Leo than Barcelona.
"I have a great friendship with him. I see him as a friend, like a normal boy. I'm amazed with what he does. I've had the luck and pride to play with him when we were kids. When I am with him, he is like one more, like a friend. He is normal, very familiar."
The Chelsea midfielder was speaking ahead of the Blues trip to Atletico Madrid on Wednesday night (27 September).
Diego Costa is expected to watch the game from the stands after Chelsea and Atletico agreed terms for the Spanish player to complete his long-awaited return to Diego Simeone's side.
The Spanish forward is very close to Fabregas and the Chelsea midfielder didn't hesitate to say that Costa will be vastly missed at Stamford Bridge.
"It's a shame for him more than anyone [that he can't play until January due to Atletico transfer ban]. Diego knew that if he signed for Atletico he could not play for a few months. It has been a difficult situation for both him and for Chelsea; it has been wrong," Fabregas said.
"Clearly I would have preferred for him to continue as a teammate. Diego will never be a rival to me. In recent years there has not been a pure striker better than him; he understood my game, read my passes and most importantly he could score from them. With Diego it is not just what he gives you on the pitch but it is his character, too. He brings a lot to the group."
Fabregas' future at Chelsea also came under scrutiny last season after he enjoyed a difficult start to the life under Antonio Conte.
However, the Spaniard says that his intention was never to leave but to turnaround the situation to prove the Italian he deserves a regular place in his line-up.
"Honestly, no," the Chelsea star replied when asked whether he ever thought about leaving the Premier League champions.
"There were some people saying I should go but I know what I can give the team and if I can play or not so I decided to stay and fight. With Antonio there is no option other than to compete and give 100 percent in every training session and each match. I was mentally and physically ready to turn around the situation. It has been like a triumph. Not everyone knows what I went through during those months."