The move comes days after Just Eat Cycles operator Serco announced it would not extend its three-year contract in Edinburgh beyond September 17, whose losses are believed to be linked to the high cost of vandalism.
Last year, around one in four of the scheme’s 550 bikes had to be repaired every week due to a combination of vandalism, wear and tear, and weather, such as strong winds blowing them over.
However, despite the problems, there appears to be a big appetite for the service, which doubled its rentals to around 250,000 last year.
George Lowder, chief executive of council-owned Transport for Edinburgh, which is in charge of the scheme, has spoken of being “incredibly proud of the scheme’s sustained growth”.
However, city council leader Adam McVey last week accused Serco – which also runs the London hire scheme – of walking away, which he said was “highly regrettable” and a “frustrating shock”.
Serco’s decision comes a year after it reported “unprecedented” growth and expanded its network of hire points to Musselburgh.
Now nextbike, which has run Glasgow’s larger cycle rental scheme with nearly 1,000 bikes for the city council since 2014, has indicated its interest in Edinburgh.
The company had bid for the original Edinburgh contract and brought a demonstration electric bike to the capital to help showcase its plans four years ago.
Managing director Krysia Solhweim told The Scotsman: "It's sad to see that the future of Edinburgh's bike share scheme is in doubt.
"Bike share brings numerous benefits to communities, including providing affordable, sustainable transport options, alongside the mental and physical health benefits that cycling brings.
"We're always looking for new cities across the UK to expand our network and we know from the success of our well-established Glasgow scheme that Scotland loves cycling.
"We'd be keen to have a conversation to see how nextbike might be able to help."
Cycling experts with knowledge of the two cities’ schemes said nextbike had successfully averted vandalism by “engaging with communities” and offering bespoke hire rates to people on low incomes suffering “transport poverty”.
The Glasgow scheme was rebranded last month as OVO Bikes as part of a three-year sponsorship deal with OVO Energy, with a further 60 bikes to be added later this year.
Serco said it was a “possibility” that an incoming operator could take over the Just Eat Cycles fleet rather than replace them with its own.
A spokesperson for the firm said: “As part of the demobilisation, Serco are working through a strategy with [city council company] Transport for Edinburgh and partners to handle the bikes appropriately.”
They also insisted: “Serco have absolutely not walked away from the scheme, and have done everything in their power to try and secure an extension.”
Sam Jones, its micromobility director, said it had “explored every route possible to find extension options” to its original contract but this had proved unsuccessful “due to factors outside of our control”.
Mr McVey has said the council was “actively pursuing options” to ensure a replacement scheme was put in place as soon as possible.