Huddersfield's takeover is "in the English Football League's hands", the club has confirmed.
"We became an EFL club formally last Friday at the AGM conference in Portugal. We are literally now in the hands of the EFL to finalise the fit and proper test," Terriers chief executive Julian Winter told Huddersfield Town TV.
"I'd hesitate to put a date on it because we are in their hands to finalise it now. This week, hopefully, things accelerate.
"Dean wanted to get the announcement out, and rightly so because it was great for him and his family to get the acknowledgement they did.
"But in technical terms, we couldn't – and still can't – conclude the takeover until Huddersfield Town became an EFL club.
"We are still in the process and hopefully coming to the final hurdle."
Hodgkinson's recent misconduct charge for betting on football matches is not expected to affect his takeover.
The founder and chief executive of Liverpool-based legal services company PURE Business Group admitted to the charge and was fined £1,500 last month by the Football Association.
The case related to 99 bets he placed on games between September 2015 and February 2019, during which time he was a football agent and a director of non-league club Southport.
It is understood Hodgkinson told Huddersfield about the case at the outset of talks with Hoyle and has kept them informed of the situation throughout.
Hoyle, who has been Terriers' owner for the past decade, will retain a minority stake in the club.
During his ownership, the club won promotion from League One and defied the odds to reach the Premier League via the play-offs in 2017 but were relegated back to the Championship this season.
"Until Phil formerly takes control, then Dean is still in control, so we are still able to get along and make decisions," Winter added.