Jardim resigned despite leading to Sporting to second spot in the Portuguese league and a place in the Champions League group stage for next season.
"We have a feeling of respect and friendship for Leonardo Jardim," club president Bruno de Carvalho said. "We've had a very good season together and we don't regret the choice."
Jardim, 39, has been widely tipped to replace Claudio Ranieri after the Italian left AS Monaco on Tuesday after two seasons.
Born in Venezuela to Portuguese parents, Jardim has made a habit of changing clubs frequently.
Since 2008, he has had one season with Chaves, two with Beira-Mar and one each with Braga, Olympiacos and Sporting.
- Sports & Recreation
- Leonardo Jardim
- Claudio Ranieri