Henderson is said to have made a conditional offer at 95p a share, made up of cash and shares, say people familiar with the talks.
An offer pitched at that level would be at a discount to Gartmore’s closing share price of 104.8p on Friday, when it announced it had begun talks with Henderson. The company listed in January at 230p per share.
A deal could be announced as early as this week.
Switzerland’s GAM Holding AG and Japan’s Sumitomo are also said to have expressed interest in the firm.
Gartmore has been hit by loss of star fund managers such as Roger Guy and Guillaume Rambourg since it floated on the stock exchange about a year ago.
Last month it said it would seek a merger or sale of the company. Goldman Sachs is handling the auction.
Neither Gartmore nor Henderson, which already has a 14.2 per cent stake in Gartmore, could be reached for comment.
If Henderson does snap up Gartmore it will be the second time it has rescued a rival in as many years. Last year it bought John Duffield’s New Star, after it was taken over by its banks.