Mr Gilbert, Aberdeen's chief executive, said the house "would love the opportunity" to run £2.1 billion Alliance Trust, which is facing a vote later this month demanded by hedge fund Laxey Partners, over whether to outsource its investment activities.
His move comes nine years after Ms Garrett-Cox quit as Aberdeen's chief investment officer for rival Morley Fund Management. She has run Alliance Trust since 2008.
While Mr Gilbert remained tight-lipped about his motivation yesterday, Ms Forseke, in only her second day as Alliance Trust chairman, played down Aberdeen's threat.
"We have not been approached by anybody," she said.
"This is not about Katherine at all," she insisted.
"Having said that, Katherine has done a fantastic job in the last three or four years."
She added: "At this point in time the board of Alliance Trust is of the view that being self-managed is in the interests of all our long-term shareholders."
Aberdeen has a similar fund in the £1.3bn Murray International trust, run by the well-regarded Bruce Stout.
Alliance Trust's house broker Numis said Mr Gilbert was unlikely to make an immediate attempt to oust Ms Garrett-Cox from the helm of the 123-year-old company.
"With assets of £2.1bn and a retail shareholder base, Alliance Trust would be a very attractive mandate," analyst Charles Cade said.
"Murray International undoubtedly has a strong track record, but we doubt whether it would look to make a hostile approach."
But Laxey Partners said: "We welcome Aberdeen Asset Management's interest and note that the performance of Murray International was vastly superior with its shares consistently trading at a premium. What an upgrade for all shareholders that would be."
It added: "How our [Alliance's] chairman in her second day in office can dismiss out of hand an approach from Aberdeen shows how little thought has been given to serious, legitimate concerns over performance, rating and costs."
About 250 people work for Alliance Trust, most in Dundee, although it also has outposts in Edinburgh and London.
Part of the argument between Laxey and Alliance is over costs.
Laxey says expenses at Alliance amount to 0.98% of the trust's assets, while Alliance says they are a below-average 0.65%.
"External managers tend to have a greater incentive to focus on short-term returns," said Ms Forseke, who is also deputy chairman of the Financial Services Authority.
In a circular to shareholders yesterday setting out its defence, Alliance said Laxey's actions had cost £2.5 million in the past two years.
A year ago Laxey's attempt to force Alliance to introduce a formal discount control mechanism to narrow the gap between its share price and the underlying portfolio was rejected after receiving the support of around one-third of investors.
"Laxey was firmly defeated then," Ms Forseke said. "If you take that and look at an improved performance, I do not see why shareholders should vote any differently this year."
She styled the battle as being between long-term and short-term investors.
Isle of Man-based Laxey's previous rebellion seemed to prompt a change of heart about share buy-backs at Alliance which has since acquired £275m of stock. This time, analysts think Laxey is unlikely to win concessions over external management of Alliance Trust.
Stephen Peters, analyst at Charles Stanley, said: "It is unlikely that a new chairman of Alliance Trust will come in and say I am essentially sacking 250 people in Dundee."
But Laxey could yet secure a compromise over its call for realised capital gains to be paid out as dividends.
Alliance Trust declined to discuss its contact with Laxey but said it would meet the firm ahead of the shareholder vote.
Alliance Trust's shares fell 0.3p or 0.1% at 372p.
Aberdeen rose 11.2p or 4.3% to 270.3p.