The 21-year-old has earned a reputation as one of the hottest prospects in Germany thanks to his 16-goal haul in 33 Bundesliga matches last season, fulfilling the potential he showed as a youth player.
Beier - a physically imposing attacker at 6ft 1in tall - has also broken into the national team setup on account of his domestic work, earning a call-up to Germany's Euro 2024 squad and making one appearance at the tournament.
Despite still being under contract with Hoffenheim for another three seasons, Beier is being courted by a handful of top European teams, and his current side are seemingly resigned to losing him before the transfer window shuts.
Both Chelsea and Liverpool have been tipped to rival each other for the 2002-born forward, as have Aston Villa and Juventus, but all four sides will seemingly be left disappointed in their efforts to win the heated battle.
Beier 'verbally agrees' Dortmund move
According to Sky Deutschland, Dortmund are currently in the driver's seat for Beier's signature, and the Germany international has given the green light to a five-year contract with BVB until 2029.
Dortmund supposedly feel that Beier is the perfect candidate to fill the attacking void left by Niclas Fullkrug's move to West Ham United, and head coach Nuri Sahin is pushing for his signature.
The Hoffenheim man is now just waiting for the two clubs to come to an agreement over a fee, and Dortmund have supposedly tested the waters with an opening bid of €25m (£21.5m) including add-ons.
Hoffenheim are holding out for a higher fee, but there is still confidence on Dortmund's side that a deal can be struck for around the €30m (£25.7m) mark, especially as Beier has made his feelings clear that he wants to join the Champions League finalists.
Beier joined the Hoffenheim youth system in 2018 and has now recorded 18 goals and four assists in 46 senior appearances for the German side, who also loaned him out to Hannover 96 for two seasons.
Have Chelsea already moved on from Beier?
While Beier is seemingly admired by Chelsea chiefs, the Blues should not be losing sleep over missing out on the 21-year-old if reports about Atletico Madrid's Samu Omorodion are to be believed.
Despite supposedly failing with a pair of offers for the Spain youth international earlier this summer, Chelsea are now rumoured to be on the verge of capturing Omorodion for a fee of around £34.5m.
The striker is believed to be on his way to England in order to complete his medical with Enzo Maresca's side, who also retain an interest in Napoli's Victor Osimhen, although the Nigerian could end up costing north of £100m in straight cash.
Napoli's desire to reunite head coach Antonio Conte with Romelu Lukaku has led to speculation surrounding a deal involving the Belgian and Osimhen, but negotiations are yet to lead to an agreement.
Chelsea are also working to find Armando Broja a new club following his unsuccessful loan spell at Fulham, and it is not impossible to envisage Marc Guiu and/or Deivid Washington leaving on loan before the window shuts too.