The Colombian has been linked with a move to a whole raft of clubs this summer, from AC Milan to Eintracht Frankfurt, Crystal Palace to Newcastle United.
Speaking after the Ibrox side's win over Derby County in a friendly on Sunday, Gerrard said: “Alfredo is a huge part of what we are trying to do here. Instead of me answering this question every single press conference, I’m going to do everything I can to put Alfredo in front of you guys.
“Then you can ask him the question whether he wants to be part of this going forward. I can only say I want him to be part of it. The decision lands with Alfredo.
The 23-year-old has previously been linked with a move to the Chinese Super League.
Rangers rejected a bid at the beginning of 2018, Morelos confirming the club as Guangzhou Evergrande.
He has since said that the English Premier League is one which he is attracted to.
Yet, over the last 24 hours, odds on the Colombia international moving to the Chinese Super League have plummeted.
Last night Morelos was 20/1 to move to the CSL but overnight it has fallen to 4/1 making it the favourite on the market offered by SkyBet.
The good news for Rangers fans is that if the transfer was to happen it would have to get a move on. Chinese clubs have until the end of play on 31 July to sign players before their transfer window shuts.