The full-back was not part of Reja's plans last season and had a disappointing campaign at Samp, failing to help them avoid relegation.
"Rome is the ideal city for me," Zauri told Radio Sei. "I would love to stay here, but only in the right conditions and I do believe those exist now.
"My contract expires in 2013 and I'd like to stay to the end of the deal. My loan to Sampdoria was purely an economic problem. I didn't consider Lazio's offer to be fair, while the Blucerchiati met my personal terms.
"I have always had a good rapport with Reja and he wanted me to stay with the Biancocelesti. I didn't reach an agreement with the President, so I left, but I will 100 per cent stay if Reja considers me important.
"Lazio are a great squad and need to be more competitive now they are in the Europa League."