Gutierrez, who has played alongside Tevez over the past four years for Argentina, insists the stalemate between the two parties cannot continue.
Tevez, 27, remains in his homeland after refusing to fly back to Manchester for talks with the City hierarchy.
And Gutierrez, whose unbeaten Newcastle side travel to Premier League leaders City on Saturday, believes the top-flight has been weakened by the absence of last season's joint top scorer.
"The boss, the club and Carlos have to come up with the best solution to this," the 28-year-old told the Express.
"It is not possible for things to stay as they are because the Premier League is losing a big player in Carlos Tevez.
"They all have to talk. Either Carlos comes back, is put in the squad in his position and picked again, or they should all decide to say 'OK, let's look for something else'.
"They have to do something because this is no good for the club or for Carlos."
Gutierrez believes his compatriot is saddened by the situation and desperate to get back onto the playing field.
He added: "It is sad for Carlos because he wants to play.
"Carlos is back in Argentina because he wants to be with his family.
"He has had a break from the game but I know Carlos will only want to play and do his bit for the team and the club he plays for.
"It is a hard situation for him."