Thompson (left) was delighted to retain the services of Levein
Craig Levein has not given up on his dream of leading Dundee United to the Scottish Premier League title after committing his future to the club.
Levein spoke to BBC Sport after signing a three-year contract extension.
"I would never say never; I wouldn't ever say that the league is an impossibility," he said
"There are a number of things that make it more difficult, obviously the spending power of the Old Firm and Hearts as well."
Levein has committed himself to the Tannadice club until May 2012.
Assistant manager Peter Houston and reserve team coach Gary Kirk have signed similar contract extensions.
The 44-year-old former Hearts and Leicester City boss insisted that while it would be a tough task to break Celtic and Rangers' stranglehold of the SPL, with a settled squad, it is not beyond reason.
"The other thing is that you start to lose players when you're doing well" he added.
"There are things that make it more difficult but I would never rule it out."
Levein, who joined United in October 2006, had 18 months left on his current contract with the Tannadice club.
He was handed an additional role as director of football at the club earlier this year.
Championship side Watford had recently expressed an interest in luring Levein back to England.
But new United chairman Stephen Thompson has persuaded his manager that his future lies with the Scottish Premier League club.
Neither of us thought that it was appropriate to continue these discussions or make any announcements while my father was so seriously ill
Dundee United chairman Stephen Thompson
Levein said: "I thoroughly enjoy working at this club and I'm genuinely excited about the future prospects for the squad of players we now have.
"I also have a great relationship with the supporters and the board.
"So, when Stephen first raised the matter of extending my stay, it really didn't take long to consult with my family and decide to accept the offer."
Levein joined United when they were languishing in the relegation position and not only ensured SPL survival that season but led them to fifth spot last term, narrowly missing out on European football.
United also reached last season's CIS Insurance Cup final before losing out to Rangers in a penalty shoot-out and are presently in fourth position in the SPL.
Late club owner Eddie Thompson - with whom the manager had a close relationship - appointed Levein, who began his career with Cowdenbeath and had a brief stint with Raith Rovers before arriving on Tayside, to the board in January.
Thomson's son and successor as chairman, Stephen, said: "I have been working closely with Craig on a number of important football related issues for some months now, but I always knew my main priority was to ensure that we secured his services for a longer term.
"We began discussions some time ago and, while it was clear at an early stage that the outcome of these would be positive, neither of us thought that it was appropriate to continue these discussions or make any announcements while my father was so seriously ill.
"However, we both now think that the time is right to move forward and I'm absolutely delighted to announce that Craig and his management team have extended their stay at Dundee United for a further period."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.