Having failed to break into the first team, he was released in July 2013 and joined Ipswich Town, who allowed him to go on loan to Bury in the second half of the 2013–14 season.

After refusing call-ups from Kosovo, in November 2015, he accepted the Albania national team's invitation to continue his international career and was named in the squad for UEFA Euro 2016.

[3] His father settled the family in Lausanne and worked in construction before joining a multi-national company that made plastic packaging.

During the 2010–11 season, manager Roberto Mancini named Veseli in the first-team squad for the League Cup Third round match against West Bromwich Albion on 22 September, where he was an unused substitute for the entire game.

[3] Before the 2011–12 season, Veseli featured prominently at the 2011 World Football Challenge but did not make any first-team appearance that year.

[5][6] However, he failed to break into the first-team at Old Trafford and Manchester United released Veseli at the end of his contract in July 2013.

He was influential in their rise from 20th in the table and fighting relegation up to 11th when he left after new manager David Flitcroft decided to include Veseli in a back three alongside Pablo Mills and Jimmy McNulty.

[16] On 21 February, he scored his first goal in professional football with a speculative effort from 30 yards (27 m) in a 3–0 home win over Doncaster Rovers.

[3] In July 2015, Veseli rejected a contract offer from Port Vale and instead signed a 12-month deal with Swiss Super League side Lugano following a successful two-week trial.

Lugano also reached the final of the Swiss Cup at Letzigrund, where Veseli was sent off in stoppage time after receiving two yellow cards in a 1–0 defeat to Zürich.

[31] However, it was a difficult season on a personal level as he injured his knee, his calf, fractured his ankle and contracted COVID-19 throughout the campaign.

[3] He played nine games as Salernitana managed to avoid relegation in the 2021–22 season, with all but one of his appearances coming under Stefano Colantuono, who succeeded Castori as head coach in October only to be replaced by Davide Nicola in February.

In October 2009, he competed in the FIFA U-17 World Cup, which was held in Nigeria, playing in six matches and eventually winning the competition as captain with a 1–0 victory over the hosts at the Abuja Stadium.

[43] Albania finished the group in the third position with three points and with a goal difference –2, and was ranked last in the third-placed teams, which eventually eliminated them.

[44] Speaking in July 2014, Port Vale manager Micky Adams stated that Veseli was "quick, he can handle the ball and he's got decent pedigree".