In the Spanish capital, Alonso was launching an exhibition featuring the memorabilia of his entire career collected by his father.
Indeed, Whitmarsh was photographed with Alonso alongside representatives of the two-time world champion's other F1 bosses, including Giancarlo Minardi, Stefano Domenicali and Flavio Briatore.
Daily Mail correspondent Jonathan McEvoy said Whitmarsh was so keen to attend Alonso's exhibition that he delegated McLaren's managing director Jonathan Neale to collect the trophy in London to mark the team's 50th year in F1.
"It is understood that Whitmarsh is keen to develop a channel of communication to Alonso with an eye on bringing in the Spaniard for the 2015 season," said McEvoy.
The news ties in with the latest comments made by F1 chief executive Bernie Ecclestone, who said he was disappointed with Alonso's performance for Ferrari this year.
"I thought he gave up a little bit which is proof that he was looking for another team," Ecclestone wrote in the foreword to the official 2013 season review.
But at the very same time, Alonso's manager Luis Garcia Abad denied the 32-year-old has already agreed to move to Honda-powered McLaren for 2015.
"What you're saying is formula one fiction," Abad, also in Madrid, told Spanish radio Marca.
"You cannot have two signed contracts, as when you sign one, you must notify the body that controls it. So it is technically impossible.
"And an unsigned agreement is not an agreement."
Asked if Alonso intends to fulfil the terms of his entire Ferrari contract, which runs to 2016, Abad answered: "Fernando has said the same this year in three press conferences in different languages."