Tottenham Hotspur, Liverpool and Manchester City all reportedly had scouts present for the recent Serie A game.
The Leeds United striker impressed in Tuesday's narrow win over West Brom.
West Bromwich Albion lost 1-0 at Leeds United last night.
Loic Remy was a target of Liverpool back in 2014, but failed a medical with the Reds.
Premier League leaders Liverpool will host Red Bull Salzburg in the Champions League tonight and Jurgen Klopp will be watching Szoboszlai closely.
Reece James is regarded as one of Chelsea's top prospects, and is just breaking into Frank Lampard's side after injury.
Tottenham Hotspur reportedly wanted to raid Dinamo Zagreb 11 years after bringing Luka Modric to the Premier League but Olmo didn't follow in his footsteps.
Liverpool boss Jurgen Klopp could recall Alisson back to his side's starting line-up.
The Liverpool defender is likely to play no part in tomorrow's Champions League encounter.
Dele Alli is not guaranteed to start tonight as Tottenham Hotspur host Bundesliga leaders Bayern Munich in the Champions League.
Arsenal drew 1-1 away at Manchester United on Monday night.