The pressure is firmly upon current Blues boss Roberto Martinez after another disappointing season for the club.
They are currently 11th in the table, a position many have agreed is far below where they should be competing given the talent in the squad.
That has led to talk of Martinez potentially being sacked, with focus on who could replace him at the club.
Hughes is one of those who are reportedly on the list, but the Welshman has refused to comment on such links, although he admits given his sides recent poor form they are a positive.
"It is just speculation and I don't encourage that," Goal reports him saying.
"The talk about jobs, I have had that against me before. I didn't like it so I wouldn't want to comment and encourage that sort of speculation against someone who is in the job already.”
“On the back of three poor performances, all speculation like that is positive I suppose!"
There is no denying that Hughes has resurrected his career at Stoke following low spells at QPR and Manchester City damaged it.
He is arguably not the name that Everton fans would want though, with them eyeing up much bigger names for the manager’s hot seat at the club.
First though they would have to sack Martinez, with no signals as yet from the club to indicate that is going to happen.