The team would also get involved in the enforcement of the City Council's car parks, dealing with stray dogs and the removal of small illegal encampments from Council land, which can be associated with anti-social behaviour and drug taking.
Cllr Keith Owen, Lead Councillor for Environment, Health and Wellbeing, said: "We are using existing staff resources to create this new team to improve the lives of those who live and visit Exeter and make it a better place to be.
"In years gone by we have in some shape or form had officers dealing with these specific enforcement issues but due to the government cutting our funding, these posts have either disappeared or been absorbed into a much wider remit with less of an on-street presence. The new team will help reverse this and tackle everyday issues that are important to the people of Exeter."
The proposal to create a new enforcement team will go before the Council's Executive on Tuesday 24 June.