Salah completed a move to Liverpool from Roma last month for a club record £37million, which could eventually reach almost £44m.
The Egypt international, who penned a five-year deal at Anfield, endured an unsuccessful two-year spell at Premier League rivals Chelsea.
And former Liverpool midfielder Hamann fears the 24-year-old winger could again take time to adapt to life in England's top flight.
Hamann also doubts Salah will arrive at the Merseyside club as a guaranteed starter due to the level of competition in his position.
"I'm not really sure what to expect from Salah," Hamann told talkSPORT. "It's clear he's a very capable player.
"But we've seen it in recent years that some of the best players came to the Premier League and couldn't adapt to it.
"So as much as I'm excited to have him, I'm also a bit cautious. That position is also probably the strongest part of Liverpool's team.
"With [Philippe] Coutinho, [Adam] Lallana, [Sadio] Mane and [Roberto] Firmino already there, I don't think it's a forgone conclusion [Salah] will play.
"There are other areas in that Liverpool team that need addressing - you look at left-back, centre back, centre midfielder and in goal.
"There are three or four positions that still need addressing and I would have rather seen them addressed before another winger came in."
Source: Daily Express