The Tigers agreed a deal with Everton at the start of the week to enable Bowler to stay put and are hopeful that Blues defender Matthew Pennington and Liverpool midfielder Herbie Kane will follow suit shortly.
As it stands, no extension has yet been agreed between Hull and fellow Championship strugglers Barnsley regarding winger Mallik Wilks staying at the KCOM Stadium for the rest of 2019-20.
But the East Yorkshire club remain hopeful of retaining the former Leeds United wingman, who enjoyed a successful loan season under the management of Hull chief Grant McCann when he took Doncaster Rovers to the League One play-offs in 2018-19.
The Tigers have an option to buy Wilks, but it expires on June 30.
The situation is more complicated regarding Marcus Maddison, who joined the Tigers on a six-month loan deal from Peterborough United at the start of 2020 - but is out of contract at London Road at the end of June.
Maddison, Wilks, Pennington and Kane are back training at Hull's Cottingham training base alongside Bowler.