The 1982 World Cup winner believes that the former Republic of Ireland boss would be the sensible choice for the Biancocelesti because of his "desire and passion"
Edy Reja is expected to take charge of the struggling Biancocelesti in the coming days, with club president Claudio Lotito poised to dispense with the services of the under-fire Petkovic, who announced on Monday that he will become Switzerland boss next summer.
However, Tardelli, who most recently worked with Trapattoni with Republic of Ireland, believes that the 74-year-old is the ideal man for the Lazio job.
"Take Trapattoni," he urged Lotito in an interview with Radio Sportiva, "and go on the safe side.
"I don't know any more than we read in the papers, but I still see Trap as a great coach: he always has great desire and passion."
Tardelli then turned his attention to former club Juventus, who earlier this month failed to reach the knockout stages of the Champions League after losing 1-0 to Galatasaray.
"To be among the elite in Europe, Juventus still don't have the players of the same value as the top three or four sides," Italy's 1982 World Cup final hero reasoned.
"I believe that they need two or three important elements to make that leap forward; otherwise if you go to see the squads of Bayern [Munich], Barcelona and Real Madrid, you'll continue to notice the difference.
"In any case, now Juve must go all out for the Europa League."
As for Sunday's Derby della Madonnina, ex-Inter boss Tardelli opined that the Nerazzurri still have much work to do in spite of their 1-0 win over AC Milan.
"I believe that there are still problems at Inter," he argued. "The gap to Juve confirms their difficulties, even if [coach Walter] Mazzarri has done a great job.
"Also, Milan don't have the quality to fight for the top three places in the championship."