Cheshire West and Chester Council wants to introduce designated busking areas for approved buskers which performers would need to book.
Joining a debate on the issue, Chester MP Chris Matheson said: "I like the spontaneity of buskers. I wouldn't want to control them."
However the city centre manager said busking can cause problems for shops.
"Not everyone is the biggest fan of somebody who's playing outside their business when they can't do business for such long periods," Peter Lewis added.
"What we are asking for is that buskers show a level of respect and concern."
Chester and the surrounding west Cheshire region drew more than 31m visitors in 2014.
Buskers in the city are divided on the proposals.
Professional guitarist David Jimenez (above), who busks in towns across the northwest England and the Midlands, said Chester was "really good for buskers" with "a lot of culture and tourists".
He added the new rules would be "a shame", saying "there have been street musicians in Chester for hundreds and hundreds of years".
But Frank, who occasionally plays his harmonica in the city for fun, is in favour of the rules.
"If we're overcrowded with buskers and it's just a mash of sound, it's not very good for the public anyway," he said.
According to a council report, buskers would need to comply with a code of conduct, which would involve an "assessment of quality". Those who comply would earn an "approved busker" badge.
Mr Lewis insisted the "assessment" would not involve auditions for buskers.
But Mr Matheson said: "I think part of the essence of busking is the artistic freedom they're given, so in my response to the consultation I'll be suggesting that perhaps we leave buskers out."
The council's consultation shows it is already considering involving working with buskers and the Equity and the Musicians Union to draw up alternative rules.
Buskers should be left out of new rules designed to improve the image of Chester city centre, an MP has said.