The message, which came from an unverified account in Henry's name, appeared to make reference to a bid from Arsenal for wantaway striker Luis Suarez, amid reports that the Anfield club have turned down a fresh offer of £40million.
It read: "What do you think they're smoking over there at Emirates?".
The post has since been re-tweeted over 38,000 times on the social networking site - and OMNISPORT understands that Liverpool are now in the process of trying to establish whether it was indeed posted by the club's owner himself.
Suarez has been linked with a move away from Anfield throughout the close-season, with La Liga giants Real Madrid rivalling Arsenal for his services.
The Uruguay international has expressed his dissatisfaction with life on Merseyside, following criticism from the English press in the wake of a string of incidents, including his bite on Chelsea's Branislav Ivanovic last season.
Manager Brendan Rodgers is keen to retain the striker's services, though, and insists that the club are not looking to sell.
Suarez's value to Liverpool was underlined once again during their pre-season triumph against Melbourne Victory on Wednesday, as he came off the bench to set up the second goal in a 2-0 win.
