The 21-year-old spent the latter half of last season on loan at League One club Charlton, for whom he scored three goals and provided six assists from 27 appearances.
Having been impressed by Millar, the Addicks were interested in taking the winger back to the club this summer, but look likely to miss out on him.
Swiss giants Basel are locked in negotiations with Liverpool over a permanent deal for the Canada international and leading the chase to secure his signature.
Talks are continuing between Basel and the Reds as they attempt to reach an agreement over a transfer fee and the overall financial package.
It is said that Jurgen Klopp’s side will insist on adding a significant sell-on clause into their deal with Basel.
Millar, who has been on the Merseyside-based club’s books since the summer of 2016, is said to be keen on a move to the Swiss top flight club.
Apart from Charlton, Blackpool, New York Bulls and Odense were also interested in signing Millar, but they all look likely to miss out on the forward.