The 22-year-old played only 12 times for the Premier League side last season and his contract comes to an end at the conclusion of the 2014-15 campaign.
Newcastle will listen to offers for Ameobi but Wednesday are likely to face competition for his signature from Sky Bet Championship rivals Middlesbrough, who he had a spell on loan with in 2012-13.
"We have spoken to Sammy’s agent," Gray said.
"He is a quality player and he has shown that by playing in the Premier League."
Ameobi previously admitted next season would be a big one for him, either getting a move away from Newcastle or forcing his way into Alan Pardew's first-team plans on a more regular basis.
“Next season’s the big one for me – it’s my opportunity," he said.
“I’ve got one year left on my contract and I’ve got to prove I’m good enough to be a Newcastle player so I’m going to be working very hard over the summer to hopefully start fast next season.
“I was fit and I was enjoying playing at that time. It was just a shame about the injury. Hopefully working over the summer will help to prevent injury and I’ll be able to show what I can do.
“I’m not a kid anymore – I’m a grown man – so I fully expect that I’ll be treated that way. I’m going to put in the effort and if I’m not good enough, I’ll have to move on.”