Newcastle open their competitive season at home to Keane’s former club Nottingham Forest at St James's Park on Saturday (3pm kick-off).
Only Liverpool, Manchester City and Tottenham Hotspur have picked up more Premier League points than Eddie Howe’s side so far in 2022.
While Keane believes The Magpies will improve on last season’s 11th placed finish, he doesn’t see them breaking into the top six and competing with the likes of Manchester United.
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When asked if Newcastle could finish higher than the Red Devils this coming season, Keane told Sky Bet: “I don’t see it, as poor as [Manchester] United have been and the big improvement with Newcastle during the second half of the season, I think it certainly helped they spent in January - maybe £85m, £90m.
"That’s a few bob and the recruitment was a big help to them, they struggled during the first half of the season but I don’t see Newcastle top six.
"It’ll be a big improvement, obviously recruitment, how much money [Howe] gets to spend. Top 10, but I can’t see top six.”
Keane captained Manchester United from 1997 until 2005 and became manager of Newcastle’s fierce rivals Sunderland the following year.
Newcastle have made three senior summer signings so far with Matt Targett, Nick Pope and Sven Botman joining the club. Meanwhile, Man United have also signed three players in Tyrell Malacia, Christian Eriksen and Lisandro Martínez as new manager Erik ten Hag looks to improve on last season’s sixth placed finish in the top flight.