Totti, 40, ended an iconic 24-year career at Roma when he departed the capital outfit at the end of the 2016-17 campaign.
It has been claimed that the Italian is considering accepting a director role with Roma, although Zeman has offered the forward the chance to continue as a professional player.
"Totti still wants to play, and they want him over in the USA," said Zeman told Radio Due. "He shouldn't be going into any ambassadorial role just yet, he needs to play and I hope he can do so in a major team.
"I spoke with him last week and he still wants to play, but it all depends on the conditions. I believe he still wants a competitive challenge, and to that end I'm always happy to give him a trial."
Totti made his Roma debut at the age of 16, and went on to make 786 appearances for the club, scoring 307 goals in the process.
Pescara, meanwhile, will play Serie B football next season after finishing bottom of Serie A last term.