FRANKFURT, July 26 (Reuters) - German real estate company Vonovia (VNAn.DE) is expected to launch a fresh attempt to buy rival Deutsche Wohnen (DWNG.DE) within weeks, having so far failed to secure sufficient shareholder backing, people close to the matter told Reuters. Vonovia on Monday said Deutsche Wohnen shareholders had tendered 47.62% of the target"s equity in favour of the 18.7 billion euros ($22 billion) offer, missing the required 50% threshold by last Wednesday"s deadline. "The CEOs of both companies still want the deal and they are looking to find a solution," one of the sources said, while another said any new offer would be launched only after Vonovia"s supervisory board had analysed the matter and signed off on it. Both Vonovia and Deutsche Wohnen declined to comment. Vonovia failed to secure the deal for a number of reasons, with some shareholders declining to tender their shares on a view that the offer undervalued Deutsche Wohnen. "Vonovia has offered a purchase price of 52 euros per share. I consider this to be significantly too low and therefore absolutely unacceptable", Michael Muders, portfolio manager at Union Investment - which holds more than 2% of DW - told German business weekly Wirtschaftswoche. A number of hedge funds tendered none or only a small amount of their holdings in anticipation of getting more for their shares at a later stage, while index funds holding about 20% of DW shares are able to tender their shares only after the minimum acceptance quota has been reached, according to their own rules. Vonovia had also agreed with Deutsche Wohnen that the latter would not tender its roughly 4% in treasury shares, to make the deal cheaper. With Vonovia failing to win over enough Deutsche Wohnen shareholders, any improvement in its offer might be a case of closing the stable door after the horse has bolted, a person close to the matter said. "Now that the wheels have come off, it will be cumbersome and expensive to get them back on", the person said. Under German law, if a target company agrees and German financial watchdog Bafin issues a waiver, a potential buyer can make a new approach immediately after a failed offer without having to wait for 12 months, with such a waiver seen as little more than a formality. The deal would create a property giant with 550,000 apartments, but has been the centre of heated debate in Germany amid tensions over soaring rents ahead of general elections in September. Vonovia had failed in a 2016 takeover attempt but this time Deutsche Wohnen"s CEO favours the deal. ($1 = 0.8471 euros)