Sir Tom already holds a 29.9 per cent stake and has made the approach through his investment vehicle West Coast Capital (WCC).
A source said: "Any offer will be for not much more than the current share price. WCC paid a lot more for the first 30 per cent."
The source suggested there would be little crossover with Wyevale. Flying Brands was launched in Jersey in 1981 as Flying Flowers and floated in 1993.
In 1995 the company bought DPA Direct, out of which it built gardeners' home shopping service Gardening Direct. The group has a database of about five million customers. Online brand Gardenline closed last year following heavy losses. New chief executive Tricia Killen hopes to move the business from Jersey to the UK mainland.