The publication explosively alleges that Jack's wife Lisa learned of his affair with Kayti Edwards, the granddaughter of Julie Andrews.
In Touch alleges the pair were spotted outside a hotel in Los Angeles on April 11.
'It was the Courtyard by Marriot', an eyewitness reportedly told In Touch.
'Jack seemed nervous and was looking around a lot.'
According to the source, Jack and Lisa, who have been married six years and share three daughters - Pearl, 6, Andy, 2 and Minnie, 3 months, have been fighting a lot, which lead to their split.
Jack Osbourne, Lisa Shelly and Kayti Edwards have not responded to In Touch's claims.