The 19-year-old has attracted plenty of interest following his excellent breakthrough season last campaign.
He made 35 appearances for Hibs, impressing with his tenacity, solidity and ability to get up and down the pitch, providing an attacking threat.
Mathie revealed Doig has the athletic potential of an “elite level athlete” but has been annoyed by clubs undervaluing the teenager.
"If Josh Doig performs how he performed last season in English League One and got to a national final, teams would be willing to spend far more money on him, rather than if he was in Scotland.
"We finished third in the league, we’re in Europe, we got to a cup final, and these bids are really disrespectful.”
Mathie explained to Vavel what he would like to see happen with the left-back and that includes ensuring he is not sold to a team to play him in their Under-23 side.
He said: "I would love it if a club were to come to me and say that ‘we think we can turn this boy into a £50M player, here’s how we're going to develop him, we’ll give you x if he achieves this, and we’ll give you y if he does that, and within a certain number of years, we think he would be at the top level of the game’.
"That makes a conversation far easier, as it becomes less of a transaction and more of a relationship.
"But right now, we feel some clubs have been quite patronising and more transactional, and it is hard.”