Manchester United will reportedly begin official talks with Ole Gunnar Solskjaer over a permanent contract at the club during the next two weeks.
Solskjaer has been in interim charge of the team since replacing Jose Mourinho in December, but his record during that time has made him the overwhelming favourite to land the job on a permanent basis.
The Norwegian has won 14 of his 19 matches in charge across all competitions to drag United back into the top-four race and reach the quarter-finals of the Champions League.
Woodward is not thought to have made a final decision on whether to appoint Solskjaer yet, but the former United striker is the clear leading candidate due to his popularity amongst the players and the supporters.
Mauricio Pochettino and Massimiliano Allegri had been early favourites to succeed Mourinho and remain in outside contention, but Solskjaer is expected to be handed the reins beyond the end of his current short-term deal.