The Blackburn Rovers attacker scored 27 league goals this season, six more than nearest challenger, Southampton striker Adam Armstrong.
His strikes included a brace on the last day of the regular campaign, as Rovers won 2-0 at Leicester City to clinch Championship safety.
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The U’s are understood to have enquired about Szmodics on January deadline day in 2022, when the 28-year-old was at Peterborough United.
At the time, he had scored just three goals for Posh in the first half of the 2021/22 campaign.
This newspaper reported at the time that Peterborough were only interested in a permanent deal, however United wanted a loan move.
Szmodics went on to join Blackburn for £1.8 million in August 2022. He scored seven goals in 41 games during his debut campaign least season, but has backed that up with 33 goals in 48 appearances across all competitions this campaign.
His form has seen him linked with a host of Premier League sides, including Everton, Brentford and Luton Town.