The Switzerland U21 international only joined the Premier League champions from local rivals Manchester City in January 2012, but has been released upon the expiry of his contract this summer.
A number of Bundesliga and Serie 'A' clubs have been credited with an interest in Veseli's signature, but according to the defender's agent, Adam Bouskouchi, his preference would be to remain 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," he told Sky Sports.
"There are a number of clubs showing an interest and he is considering his options."
Crystal Palace, Birmingham City, Middlesbrough and Wigan Athletic are among a number of Championship clubs monitoring Veseli's situation, but he will likely hold out for an offer to stay in the top-flight.
A centre-back by trade, Veseli can also operate at full-back or in a more advanced midfield role, and was tipped to make a first-team breakthrough at Old Trafford after being included on Manchester United's pre-season tour of South Africa last summer.
But, for whatever reason things never worked out, and following Sir Alex Ferguson's retirement - and the appointment of his successor David Moyes - the youngster has been released and will look to kick-start his career elsewhere.