Everton have been linked with both Newcastle United's Rafael Benitez and Stoke City's Mark Hughes.
Mark Warburton's Glasgow Rangers side were beaten 3-2 by the Scottish Championship team.
The Whites are reportedly closing in on a new manager.
Former Manchester City manager Manuel Pellegrini is reportedly in talks to become Everton's next manager.
Hasselbank led the R's to 12th in this season's Championship.
Mainz goalkeeper Loris Karius is currently undergoing a medical at Liverpool.
Tottenham Hotspur's Eric Dier is playing a key role for both club and country.
Newcastle United are currently the favourites to earn promotion from the Championship this season.
Liam Henderson has been on loan at Hibernian from Celtic this season.
HITC Sport understands Sheffield United eye new right-back.