The former Real Madrid striker was meant to be the answer to Chelsea's striker problems when he signed but he has failed to settle in London and has struggled for game time under Maurizio Sarri this season.
Should Fabregas move to Monaco, he will be reunited with former Arsenal teammate Thierry Henry, who is now their manager. The midfielder attempted to play on, but could not see out the remainder of the first half.
Fabregas reflected on his own glittering career in his post-match interview. "It feels like last week that I started playing professionally and now it's more than 15 years".
The 26-year-old forward managed to score twice in the game but he didn't look happy about it as he failed to celebrate on either occasion which didn't go un-noticed by the fans on social media.
Morata's struggle to find the net this season was summed up after 12 minutes when Davide Zappacosta's cross afforded him a free header from six yards out and the Spaniard headed straight at Luke Steele despite having the whole goal to aim at.
Fabregas added: "I saw the keeper going down in the middle of the run and I thought I had it. It was unfortunate. The day I got 100 caps for Spain I also missed a penalty, so it was destiny". Monaco have a very youthful squad and Fabregas' experience will prove to be crucial in the relegation dogfight.
He will join a Monaco side that have enjoyed a torrid season thus far, sitting 19th in Ligue 1.