The Scotland international fell out of favor under Mikel Arteta after signing former Manchester City full-back Oleksandr Zinchenko last summer.
Tierney is now second choice and has had limited playing time this season in the UAE.
Newcastle have been impressed by the move for the former Celtic defender and Stubbs believes a move north could be beneficial for both parties.
Tell Grosvenor Sport: “I don’t think Kieran will struggle for options. He will have a lot of fans in the Premier League and in Europe.
“It looks like he will have to leave Arsenal to get more playing time.
“I was surprised they signed Oleksandr Zinchenko because Kieran did very well and the fans liked him – even though he had some injury problems – but Zinchenko is Mikel’s number one and Kieran can’t join the team.
“Newcastle are said to be in the market and that sounds like a good move to me. They are closer to home too but they are a team on the rise and I could see that happening.
“They have big plans and I’m sure their ambitions will match Kiran’s.”
On Tierney’s situation, Steve Clarke explained this week: “It’s one of the things you have to deal with when you’re playing at a top-level club. I got it myself when I was a player.
“Obviously in the early days at Chelsea it was a bit easier but once the foreign influence starts to set in and the better players start to emerge, you’ll find yourself at a level where you probably won’t be picked to play every game.
“You have to deal with that. I’ve spoken to Kieran reasonably recently and he’s handling the situation really well. He understands why he doesn’t get a lot of minutes in the Premier League.
“It’s a shame he got sick last week or he would have played the game in Portugal. They have the second leg this week and I hope he starts in a few minutes.
“He just has to deal with it. That’s what he does. You have to be a good professional and work as hard as you can. His team is flying at the top of the league so, while it’s not great that he’s not playing, he can take some comfort from the fact that the team is playing.” Well “.
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