Bowen has been one of the few positives in a bleak season for the troubled Humbersiders, who are battling to stay afloat in the Championship after being relegated from the Premier League last season.
Operating primarily from the right hand side of the attack, Bowen has managed to plunder 11 goals in 24 starts for Hull this season and provided a goal and an assist as Nigel Adkins' men secured a much-needed victory over Nottingham Forest in the fourth round of the FA Cup on Saturday.
Representatives from Everton, Newcastle, Burnley and Brighton and Hove Albion would certainly have been impressed by Bowen's impactful display but, while there is apparent interest in his services from a host of Premier League sides, his elder teammate David Marshall has advised him to take a patient approach with his career development.
"I am sure Jarrod will get a move but I don't think this is the right time for him," Marshall was quoted as saying by the Daily Mail. "He's doing well, scoring goals and the rewards will come."
Everton have been hoovering up a lot of young British talent over the last few months as they look to build on the Under-23's Premier League Division 2 title win last season, while Newcastle are in desperate need of extra firepower in order to strengthen their Premier League survival bid.
The loss of Bowen could well condemn Hull to suffering their second relegation in as many years, but Adkins, whose side are only out of the drop zone on goal difference, is hoping the Tigers will be able to hold out for the next 48 hours.
"Don't answer the phone!" Adkins said. "It doesn't surprise me that Jarrod has top clubs watching him. Let's hope we can get to Wednesday."