It looked to be a two-horse race between Wycombe Wanderers boss Gareth Ainsworth and former Red Grant McCann to become Jose Morais’ successor at Oakwell.
The Star understands the club have discussed terms with three candidates – Ainsworth, McCann and one other.
Hopkin left Livingston on Thursday morning at the end of his contract and is understood to be of interest to the Reds.
The 47-year-old departed after guiding the Scottish club back to the Premiership - their second successive promotion.
Former Scottish international Hopkin rejected a new offer at the club after two and a half years at the helm.
It is understood Hopkin sees his managerial future in England after two successful seasons in Scotland.
If the Reds are to appoint Hopkin then they will have to move fast with other clubs sniffing around.
Shrewsbury CEO Brian Caldwell admitted his interest earlier this week after news of Paul Hurst’s imminent departure.
Hurst has since joined Championship club Ipswich Town following the Shrews’ play-off final defeat.
Caldwell said: “I’m open to a number of number of options just now. David’s done well at Livingston on a very limited budget. So, from that point of view, yes, that’s of interest to me.”
Like Caldwell, achieving back-to-back promotions on a tight budget would have caught the eye of the Barnsley top brass as it matches their business model.
Yorkshire rivals Bradford City and Scottish side St Mirren are also keen on hiring Hopkin.
Meanwhile, over 8,000 faithful Reds fans have already booked their season tickets for the club’s return to League One.
Un-renewed season ticket seats have gone on general sale this morning after last night’s deadline.
The cheapest adult prices start from £350, young adults and seniors from £215 and children’s season tickets from £35.