The BBC pundit, who is a regular user of the social networking site, scored 37 goals and assisted many more in 177 games in the claret and blue between 1998 and 2003.
And the former England winger still keeps a close eye on the goings on in East London.
The Hammers are experiencing what seems to be an annual glut of injuries to key players after losing star man Dimitri Payet, strike duo Enner Valencia and Diafra Sakho, key playmaker Manuel Lanzini and now Victor Moses too.
It means Bilic is left in the unenviable position of relying on injury-prone striker Carroll and the unfancied Nikica Jelavic up front.
'Backing the big man'
But Sinclair has played down concerns that the Hammers will struggle to score in the absence of their key talent and backed Carroll to come to the fore.
"Hoping Andy Carroll is going to thrive being the main man up top for West Ham for the foreseeable," Sinclair posted to the big Geordie striker on Twitter.
"All the best big man. Come on you Irons."
Many Hammers fans feel Carroll has become an expensive luxury for West Ham having made just 36 appearances and scoring eight goals in more than two years since making his move to Upton Park from Liverpool permanent for a club record £18 million.
But one thing West Ham fans will tell you is that the former Newcastle No.9 always gives 100% and when he is fit and firing there are not many better all-round forwards in the Premier League.
The problem is, he very rarely is fit and firing.
Getting back to his best
Carroll looked more like his old self in the impessive 0-0 draw against Manchester United at Old Trafford on Saturday but still did not have a single effort at goal.
It came off the back of a string of poor performances since making his latest comeback from a long-term injury.
Things are not clear cut for West Ham and Carroll as he still has four years remaining on his contract at the club.
So Bilic and Hammers fans will be hoping Sinclair is right about Carroll, even if it does mean the East Londoners have to set up differently while Sakho, Payet and Valencia are out to get the best out of the 6ft 5in forward.
His first chance to prove Sinclair right comes against in-form Stoke City on Saturday.