The French company's plans were reported in an interview with co-chief executive Jean-Francois Decaux, who suggested that the company is considering expansion in the UK market.
He said that as the last independent company in the UK, Maiden would be "a possibility for external growth". It would also be an "opportunity to gain market share".
Decaux gave no indication of any timescale for a possible bid for Maiden, which has a market value of around £119m, and the reports said that the companies were not in official talks.
This morning, a spokesman for the French outdoor advertising giant said the company "refuted" the reports, while Maiden chief executive Ron Zeghibe refused to comment.
The news of a possible bid by the French firm pushed Maiden's share price up 9.07%, or 23.5p, to 282.5p.
Analysts are understood to believe that the two companies would fit well together as both have suffered from the advertising downturn, and a merger would help them boost revenues and cut costs.
JCDecaux is said to be in a position to easily afford Maiden, while a successful bid for the UK firm would boost Decaux's chances of winning the City of London's advertising business, which is up for tender in 2004.
Shares in JCDecaux fell 0.17% or €0.02 to €11.55.
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