The newly-promoted Tigers had a €15m bid turned down, with Auxerre understood to be holding out for closer to €30m for the 22-year-old, who is also being monitored by Newcastle United.
The gap between the two valuations means Hull City face a significant task if they are to smash their club transfer record to land him, and the club are known to be targeting at least two new midfielders before the window closes.
Danois, a France U21 international, made 33 appearances in Ligue 1 last season, scoring three times as Auxerre secured their place in the division for another year. He is under contract in Burgundy until 2029, giving the French club little urgency to sell at a reduced price, and he is not the only asset they are managing this summer: forward Lassine Sinayoko has already left for Paris FC, with further departures expected as Auxerre look to balance the books.
Auxerre have shown before that they are prepared to hold firm on Danois' valuation, having already rejected an €11m offer from Bournemouth for the midfielder last summer. Ligue 1 side Rennes have also been credited with interest in the box-to-box midfielder, according to French reports, as they look to strengthen after a difficult end to last season.
Hull's move for the France youth international comes as part of a wider push to reshape their squad following promotion, with the club keen to add competition and depth through the middle of the park before the new Premier League campaign begins.
According to reports in France, Danois himself is in no rush to force through a move to Hull and is understood to be weighing up his options, holding out for a more established Premier League club or a higher-profile project in Ligue 1.
Auxerre's stance reflects a club managing a busy summer of outgoings while trying to protect the value of their prized asset, with the midfielder regarded as one of the most sought-after young players outside France's traditional top clubs.