Jack Ross is in talks to become the next head coach of the club.
Ross was mentioned when Courts left on Tuesday as the "preferred candidate" and an agreement is expected within the next 48 hours.
Courts is close to becoming the head coach of Hungary's Budapest Honved.
He was in charge at Tannadice for a year.
Courts left the club to pursue other opportunities after guiding United to a fourth place finish in the Scottish league.
He was given permission to talk to Croatian club Rijeka last week, but is now going to Honved.
Tony Asghar said the club wanted to make an appointment quickly. A few issues remain to be worked out with Ross, 46, but those are not expected to be a problem and he is expected to return to management in six months.
The fact that Ross is out of work made him the obvious choice.
He led the club to third place in his first full season, as well as the Scottish Cup and League Cup finals, and many thought his dismissal was harsh. Ron Gordon decided to fire him after two wins in 10 games.
The fact that they finished eighth strengthens Ross' case that it was a mistake to get rid of him, as well as the fact that he was involved in two promotions. Everyone at Hibs liked the style of play.
A quick appointment will be important for the club with pre-season just around the corner.
Given the upheaval of recent summers - United are searching for a new manager in June for the third consecutive season - they will hope for some continuity too, at least Courts' departure is a mark of the club's recent success.
Courts was not welcomed with open arms when his name first came up for the United job. The Federation of Dundee United Supporters' Clubs wrote to the board to make sure they understood the fans' concerns about his lack of experience and the process leading to his appointment.
Courts was the head of tactical development at United at the time. It was a big move from the club.
Courts ended Rangers' 40-game league run in the second match of the season and led his team to six wins, three draws and two losses in the first 11 games.
Courts' ability to organize a team to be difficult to beat was obvious, as United kept six clean sheets in that 11 game run. They finished with the fourth-best tally for goals conceded and only five games were decided by more than one goal.
Courts' work was done while sticking to United's core aim of using and developing young talent. He gave 16 academy players game time and the likes of Ross Graham and Kieran Freeman played more than 15 matches, even if they were the only players under the age of 22.
His ability to mold United into a disciplined side earned them fourth place and European football, a fantastic return in his debut season as a full-time head coach.
The courts had his doubts. The previous campaign, United gathered four more points than they did.
They didn't score many goals, with only two of the nine teams scoring at least one goal. Even with the addition of Tony Watt from Motherwell, who was the league's top scorer, they were not as effective in attack.
Courts' side won only five of their 17 games in the second half of the season and some would argue that he was the beneficiary of a poor quality league.
His work improving United has been noted beyond Scotland and a move to Hungary's top flight is imminent.