The £5million-rated winger, who started his career at Hereford, could move next month.
Bowen, 21, was Hull’s supporters’ and players’ player of the year last term and it would be a major blow if he left.
He has scored six times this season.
If Fulham win the race for the talent, it surely won't be the only new addition at Craven Cottage.
Claudio Ranieri replaced Slavisa Jokanovic as boss last month, and he is likely to be handed funds to ensure Premier League survival.
SunSport reported how the former Leicester gaffer has been hard at work since his arrival at Craven Cottage assessing what can be done to his squad.
And chief among the areas of concern is the lack of goals in his struggling side with much of the onus placed on Aleksandar Mitrovic to find the net.
Fulham have scored just 16 times in the league this season, with Mitrovic contributing seven of those.
But his double in the 3-2 win over Southampton are the only times he has found the net since September – and Ranieri knows he needs other options when the Serb is not firing.
The Telegraph claim one option will be to make a move for Leicester outcast Slimani – who Ranieri took to the King Power Stadium in the summer after they were crowned champions.
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