"He's on our list of targets, let put it that way," said Mariner.
Nesta, a 36-year-old centre back, has spent his entire career at Lazio and AC Milan. He left Milan in May after 10 years, saying he wanted to continue his career outside Europe, possibly in MLS.
The MLS transfer window opened Wednesday.
Mariner seemed to suggest Friday that Toronto would be a worthy destination.
"This club's a massive club," he told reporters after practice. "And I'd put it up there with Los Angeles and New York. This is a really big club and this is a fantastic city in which to live and work.
"And there's no doubt he's a fantastic player. But we'll have to see what happens."
Earlier reports had linked the stylish Italian defender to New York and Montreal. Nesta was reportedly in Montreal on Wednesday to see the Impact, who are now home to several Italian players, host Toronto.
Mariner conceded earlier this week that his 2-10-2 team needs help in defence.
"It's pretty obvious that we need a boss back there," he said. "We need somebody that can control that backline."
Despite its 3-0 win in Montreal on Wednesday, Toronto has conceded 28 goals in 14 games this season. Only expansion Montreal (29) has given up more.
Injuries have not helped the Toronto backline. Canadian international Adrian Cann and Jamaican international Dicoy Williams are both coming off long-term knee injuries.
Toronto has used 19-year-old Doneil Henry, 21-year-old Ashtone Morgan, 23-year-old Richard Eckersley and Jeremy Hall, and 24-year-old Logan Emory in its young backline.
On the payroll front, Toronto would undoubtedly have to come up with a creative way to accommodate Nesta.
It already has three designated players in Torsten Frings (US$2.41 million this season), Julian De Guzman ($1.91 million) and Danny Koevermans ($1.56 million). That means Toronto accounts for three of the league's million-dollar-plus salaries.
Nesta helped Milan to two Serie A titles and two Champions League trophies. He won the league once in his nine seasons at Lazio.
He also won the World Cup with Italy in 2006.
Toronto hosts Thierry Henry and the 9-4-3 New York Red Bulls on Saturday night.