Conway came up through the City academy and made his senior debut in April 2021 at the age of 18 and has scored 25 goals in 92 games.
He has returned to Ashton Gate having been part of Scotland’s squad for Euro 2024.
With the start of the new Championship season less than a month away, Manning said the rest of the City squad must be his priority.
“For me, I will always protect the group as we prepare to go into another relentlessly difficult season, we need people who are fully focused on us,” he said.
“I had a chat with Tommy and explained that to him. He’s working hard with the [under] 21s and making sure he’s getting his programmes right and he’s getting everything he needs.
“For me, my energy, and the staff’s energy, needs to go into the team that are going to be fighting for the club week in, week out.
“He’s indicated he wants to leave so the sooner the better, I think, for everyone involved.
“As it stands, we’ve had no offers on the table so we’ll have to see what happens.”
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