Hislop feels it's time for the USA captain to leave.
He told ESPN: "I think he'd get the management he needs at Newcastle United.
"Listen, if Newcastle come in for Christian Pulisic, if I have anything to do with advising him, I'm telling him take it.
"Let's remember Christian Pulisic has struggled to establish himself in a team that just finished 12th in the league.
"And given his stop-start and inconsistencies in English football – even dating back to his latter [Borussia] Dortmund days – right now, to get a team finishing in the top-four, top-half of the Premier League, I can't think of any other."