Peseiro was dismissed hours after his team lost 2-1 at home to Estoril in the League Cup, according to several media outlets including the three sports dailies Record, A Bola and O Jogo, plus broadcaster RTP.
They said that his assistant Tiago Fernandes took charge of training Thursday morning.
There was no official comment from the club, however, and Peseiro's comments on the match were still being carried prominently on Thursday evening.
"We know where we are and where we want to get to," he said. "This defeat doesn't take away our confidence, nor move us from the path we are on."
The League Cup is the least important of Portugal’s three domestic competitions. If confirmed, Peseiro will become the second coach to be fired by Sporting since the departure of its former president, firebrand Bruno de Carvalho.
Sinisa Mihajlovic was sacked after nine days after De Carvalho, who had appointed him, was ousted by the club members in June.
Sporting are fifth in the Portuguese league with 16 points from eight games, two behind leaders Porto, and second in their Europa League group.
Peseiro was previously at the club for just over one year in 2004/05. He led them to third place in the league and to the UEFA Cup final but resigned early the following season after some poor results.
The 58-year-old, who in June cut short a two-year contract with Vitoria Guimaraes, has also coached Porto and Braga, as well as teams in Saudi Arabia, Egypt, Greece and the United Arab Emirates.
Sporting, where five-times World Player of the Year Cristiano Ronaldo made his professional debut, are considered one of Portugal's big three clubs alongside Benfica and Porto, although they last won the league in 2002.
(Reporting by Brian Homewood, editing by Pritha Sarkar)
