Jones spent the first half of the season on loan with Notts County, having previously enjoyed temporary spells with Northampton and Oldham.
"He is someone we have monitored for a long time," said Trollope.
David Moyes was swiftly appointed as Sam Allardyce's replacement as Sunderland manager on Saturday.
Sam Allardyce was on Friday handed his dream job of managing England, 10 years after missing out on the role.
Hull are looking for a new manager following the departure of Steve Bruce.
Jose Mourinho appears set to strengthen his defensive cover with the right-back area seemingly of particular concern.
A curious case has occurred in the transfer market where a player has been purchased with no intention of using
The new Premier League season gets under way on August 13 with the big guns looking to right the wrongs