The Toffees' chairman Bill Kenwright and main shareholder Farhad Moshiri met the Dutchman at the club's Finch Farm training ground on Monday afternoon to relieve him of his duties, after Sunday's calamitous 5-2 defeat against Arsenal at Goodison Park.
The result left Everton in the bottom three with just two wins in nine Premier League games so far in what is the club's worst start to a league campaign since the 2005-06 season. Everton Under-23s coach David Unsworth will take charge of the first team as they travel to Stamford Bridge in the round of 16 of the Carabao Cup on Wednesday night (25 October).
Unsworth has taken charge of Everton before, replacing Roberto Martinez when the Spaniard was sacked in May last year and could remain at the helm until the international break in two weeks' time.
By then Everton, who have won just once in the last six games in all competitions, expect to have named Koeman's successor. Kenwright and Moshiri are already understood to have drawn up a shortlist of names, which includes Burnley manager Sean Dyche, Watford manager Marco Silva and former Bayern Munich manager Carlo Ancelotti.
However, according to the Mirror, Tuchel has emerged as Everton's number one choice and the club have already made contact with the German's representatives. However, it is understood that the 44-year-old will not be rushed into a making a decision, particularly as he could be among the candidates to take over at Bayern Munich at the end of the season.
Earlier this month, the Bavarian giants sacked Ancelotti and appointed Jupp Heynckes as caretaker manager until the end of the season. However, the 72-year-old, who has managed Bayern in three separate spells and won three league titles and a Champions League in Bavaria, is widely expect to be replaced at the end of the season.
Tuchel lifted the German Cup with Dortmund last term, after losing the final on penalties to Bayern Munich the previous year, in his first season in charge of the black and yellow after replacing Jurgen Klopp.
Under Tuchel, Dortmund reached the quarter finals of the Champions League last season, when they were eliminated 6-3 on aggregate by Monaco. Ahead of the first leg in Dortmund, a roadside bomb severely damaged the bus taking the Bundesliga team to the stadium, wounding Spanish defender Marc Bartra in the process.
UEFA and Dortmund agreed to postpone the game but Tuchel strongly disagreed with Dortmund's chief executive Hans-Joachim Watzke's decision to play the fixture the following day and left the club at the end of the season.