Team principal Whitmarsh confirmed on Friday indirect talks had taken place with Alonso's representatives with regard to the 32-year-old potentially replacing Sergio Perez.
Alonso, however, swiftly put an end to the rumours of a possible return to the team he departed in 2007 in acrimonious circumstances by expressing his desire to see out the three years remaining on his contract with Ferrari, and even to sign a new deal.
It still leaves a question mark over Perez's future as the Mexican has seemingly failed to sufficiently impress since his arrival from Sauber at the start of the year.
Despite being rebuffed by Alonso, Whitmarsh knows he has highly-rated duo Kevin Magnussen and Stoffel Vandoorne waiting in the wings.
Magnussen and Vandoorne are currently first and second in the Formula Renault 3.5 Series standings, and could make the grade in F1.
"They're in the frame," said Whitmarsh.
"We're very fortunate at the moment we've some fantastic young talent coming through, and they certainly deserve to be in F1.
"There's no doubt they will come into F1, and openly, we've spoken to a number of Formula One teams about them.
"We recognise to bring someone into a top team like McLaren, with all the expectations and pressure, is a difficult thing to do.
"When we brought Lewis (Hamilton) in that was a reasonable risk which paid off.
"There was a lot more testing back then, if you look at the amount of mileage we were able to give Lewis, than there is today.
"That's one of the problems of Formula One, one of the challenges for young drivers.
"But in Kevin and Stoffel we've the two hottest talents not in F1, but it is our ambition to get them there."
Earlier on Friday, Whitmarsh had expressed a desire to speak directly to Alonso, and that he would be open to the opportunity of him coming back, despite what occurred six years ago.
On that occasion, Alonso threatened to divulge information relating to the 'spygate' saga if he did not receive number one status ahead of then rookie team-mate Lewis Hamilton, resulting in his exit after just one contentious season.
Although water under the bridge now, asked whether a move to McLaren was attractive, Alonso replied: "Not really. I love Ferrari and I want to stay until the end.
"It's nice to hear comments from all the teams and team principals every year saying they respect my job, my professionalism, and especially from McLaren.
"There were so many rumours we had a lot of problems that year (in 2007). I have always said I had no problems with anyone.
"It was just the philosophy of the team, and one man in the team no longer there (referring to former team principal Ron Dennis).
"It's good to have this compliment, but there is no intention. Three more years in Ferrari and I hope many more to come. If we can extend the contract, that will be my focus."