The Switzerland international has attracted the interest of the Bundesliga side, as well as Juventus and Everton, but his club values him higher than the offer tabled.
Basel have rejected a $28 million offer from Wolfsburg for Breel Embolo.
The 18-year-old striker has attracted widespread interest after developing through Basel's academy and making his international debut for Switzerland against the United States earlier in March.
Wolfsburg, Everton and Juventus are all interested in securing the services of the teenager, although it is the Bundesliga side that has made the first move with an offer of around $28M.