Cabinet members backed the project when they met at the city’s Guildhall yesterday.
Tory opposition councillors also welcomed the idea, but asked for more details about how the scheme will operate.
The council aims to link up with a solar power company that will install the panels, which could cost up to £14m – paid for by the firm.
The idea is that the firm’s profits would come from sharing in the money received from the electricity generated by the scheme.
Council coffers could also be boosted, while tenants in the houses with panels might see annual fuel bills drop by £85 to £120.
Cllr Lucille Thompson, Cabinet member for communities, said it was hoped that the benefits of the scheme would be shared with all council tenants. The authority has some 5,000 properties, of which 2,000 might have suitable roofs.
The Cabinet voted to approve the start of the bidding process, which is likely to take at least five months.
Council chiefs will then make a decision whether to push ahead with the scheme early next year.