The Norwich City manager has quashed speculation that the 24-year-old striker is set to move to the Scottish champions on a season-long deal this summer
Vaughan signed for the Canaries from Everton last summer but has seen his time at Carrow Road beset by a serious knee injury, which has restricted the 24-year-old to just five appearances.
The former England Under-21 international has been linked with a temporary move to several Championship clubs as well as the SPL Champions, but recently-appointed boss Hughton insists there has been no contact.
He told the Eastern Daily Press: "There is nothing in that. That is news to me. What will always happen is that names are going to be mentioned, in or out. What I have to do is formulate the squad I want come the start of the season, the end of the month.
"James has done well in the period of time that he has been with us since the start of pre-season. He is pushing for a place like the rest of the lads.
"At this moment I have got five forwards that are all pushing for places and want to be part of the plans and they are decisions I need to make over this pre-season period."