At least two new faces are due to arrive at Anfield this summer.
But Evans, who led the club to the 1994-95 League Cup, feels that mass changes would be detrimental to Liverpool's progress.
Klopp's predecessor Brendan Rodgers made seven permanent signings last summer, and eight the year before that, but Evans is pleased with the German's patient approach so far.
"When he came he said you’ve got to give me time and that’s fair enough at the end of the day," the Bootle-born ex-boss told the Alan Brazil Sports Breakfast show on Thursday. "He didn’t rush into buying loads of players.
"Obviously at the end of the season he’s going to bring players in and I’m hoping not too many. Brendan brought in eight or nine players and sometimes that can be really difficult to manage.
"It’s not a rush job, you can’t do it in five minutes, it’s going to take maybe a year or so and Liverpool fans have come on board with it."
Klopp has already made two signings ahead of next season, securing deals for Red Star Belgrade midfielder Marko Grujic and Schalke 04 defender Joel Matip.
However, with Steven Caulker's loan expiring, along with the contracts of Kolo Toure, Jose Enrique, Jordan Rossiter and Joao Carlos Teixeira, more are expected to follow.
It was reported by the Mail on Wednesday that Liverpool are working on a deal for 15-year-old ADO Den Haag defender Abdallah Aberkane, who's been capped five times by Holland's Under-16s.