Lazio are still winless in Serie A after two rounds of fixtures and Reja was jeered by his home fans during the club's recent 2-1 loss to Genoa. Lazio drew with AC Milan before Sunday's defeat.
Reja met with club president Claudio Lotito after training on Monday to discuss his departure from Lazio.
"I did not accept the resignation and would not let the coach go," Lotito told Sky Sport Italia.
"As long as I am the president, the coach will be untouchable. Reja just wanted to express his unhappiness in a city that does not love him."
Reports indicate that a final decision on Reja's situation will be revealed during a press conference on Tuesday.
Luigi Del Neri and Rafael Benitez are among the high profile managers already being linked with the job should Reja quit.
Lazio will be looking for a first league win of the campaign when they travel to Cesena on Wednesday night.