Thordarson was appointed as Steve Holland's successor in December
Crewe Alexandra chairman John Bowler has said Gudjon Thordarson is fully responsible for the first-team set-up.
Thordarson became manager when technical director Dario Gradi stepped down, after being in caretaker charge.
Speaking at a fans' forum on Monday evening, Bowler told BBC Radio Stoke: "He knows what he wants, he makes the decisions, we are fully behind him.
"[We] have started to discuss plans for next season, it will be down to him who he wants to keep and bring in."
Crewe have moved out of the bottom four of League One since Thordarson was appointed as the successor to Steve Holland in December.
Thordarson became the first manager to be appointed from outside the club in 25 years after the board of directors decided to make a fresh start following Gradi's retirement from club management and the departure of former academy coach Holland.
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