The news comes after it had emerged that Gerrard was in talks with Liverpool over an astonishing move back to Merseyside during the MLS close season.
Klopp has reportedly told Gerrard that he is happy for him to return and train with the club at Melwood, but any move containing actual playing capacity seems unlikely.
The former England international was scheduled to arrive in London this morning, before transferring on to Liverpool.
Gerrard has previously stated his desire to work as a player-coach at Liverpool, but that the potential to do so could only happen after he announced his departure from the club.
By Ollie Carroll