Andy Carroll is on the brink of joining West Ham permanently after passing a medical with the Premier League club.
Brighton have threatened to take action against the LMA as the dispute with Gus Poyet rumbles on.
Bristol City manager Derek McInnes has been relieved of his duties.
Director Jon Lansdown said in a statement: "This is a decision we felt we had to make for the good of the football club.
"Derek has been a pleasure to work with; he's disappointed but he understands the decision.
"We want to give ourselves the best possible chance of getting out of the situation we are currently in and we've got 20 games to do that."
The 41-year-old left St Johnstone to take the Robins job in October 2011 and kept them in the Championship during his first season in charge.
But the Ashton Gate outfit have struggled this term, winning just six out of 26 league matches as well as being dumped out in the first round of the League Cup and third round of the FA Cup.
The heavy loss inflicted by Leicester proved to be the final straw, with McInnes dismissed after losing 31 of his 62 games in charge.
Assistant manager Tony Docherty has been asked to take training on Monday and the club will hold a press conference on the same day.