The German texted the former Borussia Dortmund man over his decision to join Schalke this summer, but received no reply
The Ghana international used to ply his trade for die Schwarzgelben, but appeared to put his loyalties aside by completing a switch to their local rivals from AC Milan on Saturday.
And Klopp has wasted no time to take a dig at the midfielder, who spent six months under his tutelage.
"I wrote him a text message: 'Why Schalke????????' I'm really surprised," the 46-year-old revealed to reporters.
"At 11.01 am I wrote that to Boateng, with eight question marks. Boateng was a good guy, until this morning.
"But I got no response. Do not be ashamed, it's ok [directed at the €10 million signing]."
Boateng, 26, spent the 2008-09 season on loan at Signal Iduna Park from Tottenham and immediately won over Klopp with his performances.
However, last season's Bundesliga runners-up could not work out a permanent deal with Spurs, with Boateng subsequently moving to Portsmouth.
The midfielder was handed his debut for Schalke during Saturday's 2-0 victory against Bayer Leverkusen.