The Hungary international will pen a contract until the summer of 2017 with his new club once he passes his medical
The Champions League hopefuls were keen to add some more depth to their squad and they see the 25-year-old as the ideal signing to strengthen their attack.
The Hungary international will sign a four-year deal with Schalke upon completion of his medical tests after they triggered his €8 million (£6.83m) release clause.
"He is currently undergoing his medical. We have an agreement with Mainz and are currently taking care of the paperwork," Heldt told reporters.
"Adam has a great mentality, always works hard and is eager to improve.
"We failed adequately replace Klaas-Jan Huntelaar adequately during his absence last term. We can make the next step forward with Szalai. It's crucial that there's competition for places."
Szalai joined Mainz from Real Madrid in the summer of 2010 from Stuttgart and had since developed into a key player for Thomas Tuchel's side.