The 26-year-old winger has registered on the transfer radar of English clubsfollowing a number of assured displays for Bundesliga outfit RB Leipzig.
He has admitted to being a big fan of Premier League football, having sparked talk of interest from Manchester United in the past, but has seen no official offers tabled.
That situation may change this summer, once World Cup duty comes to a close, but Mjallby believes the step up a title-challenging team could be too big.
The former Celtic defender told BetStars ahead of a quarter-final clash for Sweden against England at Russia 2018: “Emil Forsberg is the one player the team rely on to do the unexpected for Sweden.
“He’s a very good player, but I’m not sure if he would be able to break into one of the top sides in England.
“He’s done well in Germany, but the top four in England are very good sides.
“He’s a good player and it will be good for him to be playing against top-class players, but it’s hard to say if he would break into one of the top four sides in England at the moment.”