But Hearts have responded that Stendel was a free agent when they approached him and assured fans they would defend any legal action “in the strongest possible terms”.
The Ladbrokes Premiership club announced on Saturday that Stendel had signed a two-and-a-half-year contract to be their manager after protracted negotiations.
Barnsley co-chairman Paul Conway had earlier demanded compensation after claiming Stendel was still under contract at Oakwell, despite the club announcing a “separation” on October 8.
And the Sky Bet Championship club vowed to step up their case, less than 24 hours before Stendel was due to begin work at Tynecastle.
A club statement read: “Early in the season, Daniel Stendel entered into negotiations with a rival Sky Bet Championship club to take over their managerial post and recruited other members of contracted Barnsley Football Club staff to follow him.
“Never once did Mr Stendel seek approval or alert members of the club’s board to these discussions. Only when approached by the board was there any sign of acknowledgement.
“This was a clear violation of Mr Stendel’s contract and created additional unnecessary distractions for our club which was recently promoted to the Sky Bet Championship.
“This event, coupled with numerous other issues, led to the removal of Mr Stendel as head coach.
“Out of respect for his contributions to the tremendous 2018-2019 season, we wanted to settle this matter privately and amicably out of the eye of the public.
“After two months of unproductive discussions (and the subsequent public announcement by Heart of Midlothian that he has joined them as their new manager), the club cannot wait any longer in speaking to its fans.
“More recently we have attempted negotiations of a settlement with Heart of Midlothian Football Club for the services of Mr Stendel, Chris Stern and Dale Tonge to no avail.
“The club will continue to vigorously defend its rights against all parties involved in tampering of club staff so the club recovers all damages incurred. All recovered damages will be reinvested in our squad.”
Stendel arrived at Edinburgh Airport on Monday evening and is due to be unveiled as Hearts manager on Tuesday afternoon.
A statement from the Edinburgh club read: “We would like to reassure our supporters that we have followed all proper procedures in appointing Daniel Stendel.
“He was not an employee of Barnsley Football Club when we first consulted him and there is no basis on which Heart of Midlothian Football Club is liable to Barnsley Football Club. Misleading reports and statements to the contrary elsewhere are entirely false.
“Should any claim be commenced against Heart of Midlothian Football Club, it will be defended in the strongest possible terms.
“We are looking forward to supporting Daniel in what we hope will be a long and successful tenure at Heart of Midlothian.
“Given that we consider any threatened claim to be entirely without merit, we do not propose to comment further on this matter.”