Huddersfield, who finished 10th in the First Division this season, have been linked with moves for the former Liverpool manager, Roy Evans, and the Sheffield United manager, Steve Bruce, in recent months, but they will invite applications for the post, with Bruce thought to be the favoured option.
Bruce has been told he has no money to spend at Bramall Lane and will have to sell, and the former Manchester United captain is disillusioned at having to work within a tight budget. However, Bruce would want a severance payment to go and could also be the target for other clubs.
Huddersfield aim to make the first move and offer Bruce a job with better prospects and money to invest on top players.
Barry Rubery, who made his fortune supplying the hardware for BSkyB dishes, took over as owner of Huddersfield in January and no sooner had he arrived than Jackson's job was said to be under threat.
A total of pounds 2.5m was believed to be available for new players initially, with the Nottingham Forest centre-half Craig Armstrong and the Bournemouth left-back Jamie Vincent signing for a combined amount of pounds 1.25m.
However, their arrival did not help Huddersfield's push for the play- offs and they finished the season with Sunday's goalless draw at home to Crewe.
When Jackson and his assistant Terry Yorath were appointed in October 1997, Huddersfield were rooted to the foot of the First Division, but they avoided relegation and led the table at the start of this season. The form was not sustained, though they did reach the last 16 of the FA Cup before being beaten by Derby.
Ian Ayre, who was named as the new Huddersfield chairman at the weekend, said: "We would like to place on record our appreciation for Peter's hard work, dedication and passion for the club.
"Huddersfield Town have made no secret of their ambitions for the Premiership and in trying to achieve these goals we are keen to ensure that we do this with the highest confidence in all key positions. Under these circumstances we believe it is in the best interests of the club to appoint a new manager.
"Contrary to speculation in the media, we do not have a successor lined up and indeed we do now wish to invite applications for the vacancy."Reuse content