The phrase "message saying that" is correct and usable in written English. You can use it when you want to indicate that someone communicated a certain idea by sending a message. For example: I received a message saying that the party was cancelled.
And on Monday he issued a message saying that he feared his crew had been beaten.
Saturday were greeted with a message saying that microblogs contained "many rumors and illegal, destructive information".
She called and left a message saying that Ms. Sarf wanted to speak with him.
Three hours after submitting the paper, Bartneck received a message saying that it had been accepted.
The site's original address at KickAss.so, based in Somalia, now shows a message saying that the site has been banned.
Visitors to the affected services were just shown a message saying that the site could not be accessed.
In Frankfurt, Wolfgang Schäuble, Germany's flinty finance minister, reiterated his boss's message, saying that haircuts were against E.U. rules.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union