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...
1. Nuno secures next move
Former Wolves boss Nuno Espirito Santo has completed a shock move to become the manager of Saudi Arabian side Al-Ittihad. (Various)
2. Saints lead Aribo race
Southampton have ‘emerged as frontrunners’ in the race to sign Rangers midfielder Joe Aribo. (Daily Record)
3. Irons have Onana bid rejected
West Ham have had a £19.8m offer for Lille midfielder Amadou Onana rejected, with the French club reluctant to sell. The Hammers remain interested. (Dharmesh Sheth)
4. Broja on Everton radar
Everton have made an approach to sign Chelsea forward Armando Broja this summer, with Newcastle United also keen. (Sky Sports)