An agreement with the German, who left Oakwell in early October, is close, according to reports in Edinburgh and the 45-year-old is expectred to be confirmed in the next 48 hours, barring any late hitches.
Hearts hope to have Stendel in the Tynecastle Park directors' box on Wednesday night against Livingston.
Austin MacPhee is expected to remain in charge of the Hearts team for the Livi game.
Stendel is said to wait to bring two assistant coaches, Chris Stern and Dale Tonge, with him to Tynecastle, with the pair recently leaving Oakwell.
Stendel and his representatives had been in dispute over a severance package after he parted company with Barnsley - with his contract due to run until next summer.
Reports in the Scottish capital say that Barnsley have contacted Hearts to seek compensation for Stendel.
Both parties are in dispute over a severance package and the Barnsley co-chairman Paul Conway has contacted Hearts seeking compensation for Stendel, according to reports in the Scottish capital.
Conway, speaking to the Daily Mail, claimed: "We still have a valid contract with Daniel Stendel until the end of the season.
"There is already a tampering issue with us concerning his existing contract. And if anybody else is tampering with our rights, we are going to expect compensation.
"Hearts have our letter and we have notified them and, if they want to hire Daniel, that's fine, that's their choice.
"But they either pay us now or we will file a claim against them. And if any club wants to fight it, we will win."