O'Brien is heading up a strategic green and open spaces board on saving parks on behalf of the city council, which is approaching a budgetary "cliff face". By 2017-18 the city expects to have insufficient money to run even its statutory services and not a penny for parks.
Dozens of suggestions were put forward as solutions to funding Liverpool's parks, and O'Brien did consider the idea of sounding out philanthropists and business as is done in America in what is known as corporate social venturing (CSV).
"It does not exist in this country," O'Brien told Horticulture Week. "I have not in all my travels seen one single example where a big hitter has stood up to the plate and said 'we'll look after that park'. I don't think that culture exists here."
So what do those in the sector think? Parks consultant Dr Sid Sullivan says the problem is not reluctant tycoons but an aloof parks sector. CSV "is a rare beast", he said. The UK parks movement is "unwilling and insufficiently nuanced" in areas prominent to the US philanthropic movement such as naming rights.
"Most approaches I've seen for large-scale funding from philanthropic sources are more focused on 'what's in it' for the parks service than the benefits to the philanthropist. Moreover, few leaders have experience of wooing and persuading donors, which needs a different mind and skill set."
Sullivan insisted that he is not of the "bleak outlook brigade" and has no doubt parks philanthropists are out there. But the sector must first produce a plan that is "plausible, skilful and attractive" for social investors.
Philanthropists are not just a Victorian throwback. An £800,000 legacy left by an Aberdeen woman in 2014 has been used to pay for improvements to Duthie Park, including replacement greenhouses, the refurbishment of two play areas and the creation of a new play space.
A year before that, civic society Sid Vale Association was left a £2.3m legacy from a man who loved Sidmouth and whose dying wish was to ensure the care of its plants. The association administers a fund in his name.
In 2012, Nottingham and Birmingham City Councils and Birmingham Open Spaces Forum trailblazed a new funding approach in response to the same funding cuts that now threaten Liverpool. The Green Places Fund was initiated by the now defunct parks charity GreenSpace. Each pilot aimed to attract £1m and coax latter-day philanthropists. Businesses in the city such as Capital Shopping Centres and Carillion agreed to contribute, with coffee chain Barista donating £5,000. The fund died with GreenSpace a year later.
Birmingham Open Spaces Forum vice chair Emma Woolf said: "We were drawing up terms and conditions when GreenSpace went under. Nothing happened with the fund - it went nowhere. There are few examples of philanthropic giving, unlike America where some big parks are funded almost entirely by philanthropy."
Tax is a key difference between the UK and the USA. Whereas the UK tinkers with Gift Aid, philanthropic giving in the USA attracts serious tax breaks. Wealth still does occasionally filter through. Last year the Friends of Cotteridge Park group in Birmingham was left a £2,000 bequest.
Bournemouth Parks Foundation, meanwhile, launched last year to protect and look after local parks and is trying to encourage people to leave cash legacies to the charity in their wills. Programme manager Theresa McManus said the response has been poor but the outlook is good.
"We experimented with legacy giving by establishing a free will offer with a firm of solicitors and advertised this in the local paper and on social media. But we haven't had enough time to establish a broad base of support."
In the meantime, supporting parks is part of a "wider cultural shift" that will not happen overnight, she said. But in its first year the foundation received pledges of £40,000 for an aviary restoration project - half given as £1 donations and the rest as individual donations of larger sums.
McManus said: "Will philanthropists come forward? People still haven't come round to the so-called 'Big Society' notion that individuals and groups will have to contribute to make up spending shortfalls. But I remain hopeful and in the first year of our existence the indicators suggest they will emerge."