Sky Sports understand that a number of Premier League and Championship clubs are following Veseli, who departed United at the end of the season.
The Swiss Under-21 intentional was highly regarded at Old Trafford after he joined the club from rivals Manchester City in January 2012.
He progressed well and was included in the first-team squad for their pre-season tour of South Africa.
Veseli, who is a centre-half by trade but can play in midfield or at full-back, is now hoping to remain in England, although there is also interest from Serie A and the Bundesliga.
Crystal Palace, Birmingham, Middlesbrough and Wigan are all being credited with an interest in Veseli.
The player's agent Adam Bouskouchi confirmed Veseli was looking to stay in England.
"Freddie wants to stay in England, he has been here since 2008 and he feels he is ready to push for a first-team place somewhere," Bouskouchi told Sky Sports.
"There are a number of clubs showing an interest and he is considering his options."