Stephen Rawlinson, an analyst with stockbroker Peel Hunt, said Amec had indicated that it wanted to sell Watson as part of a focus on predictable revenue streams.
Watson, which has a turnover of £40m, has been a highly profitable business but has struggled recently.
Rawlinson said: "Selling off part of the business could suit it. Either it cannot get someone to pay what it wants for the whole business or it thinks it may have an upside in the future, so it wants to keep a bit."