Bryan Redpath stepped down from the post last month, with forwards specialist Carl Hogg taking charge for Gloucester's final two league games of the season against Sale Sharks and London Irish.
Hogg has expressed an interest in succeeding Redpath, who is expected to land Sale's top job following weeks of speculation.
Gloucester have now established a shortlist to fill their vacancy. Talks have taken place with candidates in the United Kingdom and the southern hemisphere.
Names that have been linked with the post include former Bath boss Steve Meehan, current Scarlets head coach Nigel Davies and ex-Swansea coach John Plumtree, who heads up the Durban-based Sharks in South Africa.
"There has been a lot of work going on and we are making some very good progress," Nottage told the club's official website.
"We are now down to a much shorter list with, realistically, four options available to us. We are handling the process carefully and doing things by the book.
"Carl (Hogg) has expressed an interest in the role of head coach. He has met with several members of the board and presented his thoughts, and that will be taken into account when we come to make a decision."
Gloucester's first-team squad report for pre-season training in the third week of June, and Nottage is confident that a coaching appointment will be made before then.
"We quoted a timescale of the end of the month," he added.
"At this point in time we are still on target for that date."
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