The club, 19th in the Premier League when Howe took over, finished 11th in the table last season after a remarkable mid-season turnaround.
Newcastle have since recruited Sven Botman, Nick Pope and Matt Targett, and former ex-United midfielder Hamann believes an eighth-placed finish will be the minimum for the club next season.
“Nick Pope’s a very good signing, but, if I was Eddie Howe, I wouldn’t have looked at strengthening the goalkeeping department,” Hamann told Genting Casino.
“Matt Targett’s a good signing, and there are probably two or three more coming. There are a lot of names floating around, and we shouldn’t forget that they finished in the top five or six in the second half of the season.
“I think Newcastle will finish in the top eight. Whether they can finish higher than that depends on who else they bring in.
“Newcastle have a lot of potential, and, with the funds they have available now, everyone expects them to be in the Champions League in the next three to five years,” said Hamann.
“Nick Pope has probably signed expecting to play in the Champions League with Newcastle, so I’m not surprised that he chose to sign for them.”
Check out the latest Premier League transfer speculation below...
5. Adams deal complete
Leeds United are ‘set to sign’ RB Leipzig midfielder Tyler Adams for total fee of £20m, with the deal already ‘completed’. (Fabrizio Romano) | Getty Images
6. Albion want Benda
Brighton and Wolves are plotting moves for Swansea City goalkeeper Steven Benda. (Football Insider) | Getty Images
7. Spurs eye Depay
Tottenham are considering a move for Barcelona forward Memphis Depay, who could leave for around £17.2m this summer. (Sport) | Getty Images
8. Ake free to leave
Man City have told Newcastle United target Nathan Ake that he is free to find a new club this summer. (Football Insider) | Getty Images