Earlier this month, Hamburg sacked Josef Zinnbauer after just six months at the helm, putting their director of football Peter Knabel in charge until the end of the season.
They made the move after a 1-0 defeat to Hertha Berlin on March 20 left the northern Germany club inside the bottom three of the Bundesliga having failed to win any of their last six games, including an 8-0 humbling at the hands of leaders Bayern Munich.
Tuchel has been lined up to take over in the summer but Beiersdorfer believes the 41-year-old former Mainz manager, who is currently on a break from management after leaving his post in May 2014, will be heavily sought after.
Tuchel spent five years in charge at Mainz from 2009 and saw them finish fifth in the top-flight standings the following season, also helping the club clinch a Europa League spot last term after finishing seventh.
“Many clubs in Europe consider him as a great coach,” Beiersdorfer told Kicker, adding that Tuchel was one of many “coveted people who have delivered exceptional work”.
But he remained confident Hamburg might get their man, saying: “Thomas has not spoken to any club, so there is a chance.”
Zinnbauer was appointed at the Imtech Arena last September as a replacement for Mirko Slomka with Hamburg in serious relegation danger, but – six months on – they are in an equally worrying position.
They sit just two points off the bottom of the table but are level on points with 15th-placed Freiburg and Beiersdorfer is confident they will avoid relegation.
He added that a final decision over Tuchel was currently “not met” because: “We must see to it that we get our current problems under control.”