There is currently a host of speculation surrounding Beier's future, with Chelsea also thought to be keen on securing his signature this summer.
According to German journalist Florian Plettenberg, Villa have launched a bid for the striker, although it is unclear whether the offer matched his €30m (£25.3m) release clause.
Beier has scored 18 times and registered four assists in 46 appearances for Hoffenheim in all competitions, including 16 goals and three assists in the Bundesliga, with those goal contributions coming last season.
Hoffenheim are seemingly facing a huge battle when it comes to keeping hold of the striker, with Bayer Leverkusen also believed to be keen on his signature.
Leicester 'eyeing Ayew deal'
Meanwhile, Leicester City are reportedly keen on signing Crystal Palace attacker Jordan Ayew during this summer's transfer window.
According to the London Evening Standard, Palace are considering allowing Ayew to depart during the current market, and Leicester have now made a formal approach.
Ayew, 32, has scored 23 goals and registered 22 assists in 211 appearances for Palace since making the move to Selhurst Park from Swansea City in July 2019.
The forward was again an important player for the Eagles during the 2023-24 campaign, scoring four goals and registering eight assists in 37 appearances.
Ayew has entered the final year of his contract with Palace, so he is expected to be available for a cut-price fee.
Everton 'showing an interest in Sosa'
Elsewhere, Everton are reportedly preparing to battle Nottingham Forest for the signature of Talleres attacker Ramon Sosa this summer.
The 24-year-old is believed to have been a January target for the Toffees, and the club are now said to be considering reigniting their interest.
According to TEAMtalk, Sosa is determined to make the switch to the Premier League this summer, and he could be offered the opportunity to move to Goodison Park.
The Paraguay international has scored 17 goals and registered 13 assists in 56 appearances for Talleres in all competitions.
Sosa has another two years left to run on his contract, but he is widely expected to move on during this summer's transfer window.