The Hungary international will ink a contract until the summer of 2017 with his new club once he passes his medical.
The Bundesliga contender was keen to add some more depth to the squad, and it sees the 25-year-old as the ideal signing to strengthen the attack. The Hungary international will sign a four-year deal with Schalke upon completion of his medical tests after the club triggered his 8 million euro 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 to adequately replace Klaas-Jan Huntelaar 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. He scored a team-high 13 league goals, which tied him with Bayern Munich's Thomas Muller for seventh-most in the Bundesliga.