Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
The 19-year-old, who left Tynecastle earlier this summer before the club entered administration, is Pat Fenlon's fourth signing of the summer.
Mullen has represented Scotland at U17 level and joins Owain Tudur Jones, Liam Craig and Ryan McGivern as Hibs' summer signings.
A statement on Hibernian's website said: "Hibernian can confirm the club has signed defender Fraser Mullen on a one-year contract.
"A former Scotland under-17 internationalist, right-back Mullen, 19, agreed the deal on Saturday morning and has become the club's fourth arrival during the summer transfer window."
Hibs will depart for a training camp in southern Europe on Monday afternoon following their 1-1 draw with Dumbarton in their first pre-season friendly on Saturday.