They plan to share horticultural expertise and have identified similarities including staging large events such as the Isle of Wight Festival and the Hyde Park concerts.
A management team from the Royal Parks visited the island this week for a three-day tour to discuss a formal partnership with the council's parks and countryside department.
Royal Parks chief executive Mark Camley said: "This is an excellent opportunity to explore ways in which we can work together and look to provide a better experience for our respective park visitors."
The two bodies aimed to draw up the partnership agreement at a workshop at Ventnor Botanic Garden. The garden's curator Simon Goodenough said: "It is one of the most exciting partnerships ever explored. Over on the island, especially on the southern tip, we are a bit removed from mainstream horticulture.
"To have a working relationship with an organisation as big as the Royal Parks would be fantastic."
Goodenough said the link would be mutually beneficial: "We can offer the Royal Parks experience of establishing a strong 'green gym' programme through our primary healthcare trust as well as setting up a highly supportive Friends group. We are also earmarking climate change while growing plants in a milder climate.
"In turn, the IOWC would be looking for guidance from the Royal Parks on devising a green space strategy for the whole island."
The two bodies will produce a list of objectives, which are likely to include sharing best practice, joint training and development, community horticulture and the exchange of biodiversity and landscape management expertise.