The young Slovakian has been a regular on the bench for City this term but actual time on the pitch has been harder to come by.
Recognising he is trying to earn a place at this summer's World Cup and realising opportunities will be even further reduced once the campaign reaches its critical stage, Mancini has told Weiss he can seek a move.
Bolton's new boss Owen Coyle is among those who have expressed an interest in the 20-year-old, although the final decision will be left to the player.
"It is possible Vladimir will go somewhere on loan,'' said Mancini. "He is a good young player who is going to be important to this club in the future.
"But he needs to play. We have not decided where though. That will be Vladimir's choice.''
The fleet-footed winger has impressed with substitute appearances in the Carling Cup and was given his first start by Mancini in the FA Cup third round victory over Middlesbrough.
He has started four games for Slovakia - the national team boss is Weiss' father, also called Vladimir Weiss - and will be hoping to cement his place in the country's World Cup squad.