Former City captain Kompany urged Messi to make the move, saying that such a transfer would be "incredible" for the club.
The Belgian said, "It'd be incredible for the club to have a player like him — he could help them take the next step by winning the Champions League.
"I know (Pep) Guardiola's way of thinking, so I can well imagine the two of them will still have a rapport.
"If Messi has decided to leave Barcelona then I can only respect his decision."
Kompany added: "Let's be clear — as a City fan, I hope Messi joins them.
"I can imagine Pep and Messi still have one another's phone numbers. So they can give one another a call."