Mercedes team principal Toto Wolff said recently that he would understand if Hamilton had a desire to switch to the Scuderia.
When he visited the TV pen after the news conference, Hamilton elaborated further and said the humbling message had helped refocus his efforts after a disappointing qualifying performance had seen him beaten to pole position by Mercedes teammate Valtteri Bottas.
Hamilton has been repeatedly linked with a move to Ferrari across his career and said of a switch to Maranello in 2017: "It's definitely a dream for every driver, including me".
The Briton's Mercedes contract - reportedly worth £40million per year - expires in 2020 and Wolff even claimed to have discussed a potential move with the five-time Formula One champion.More news: Four disappointing scenarios for 2019 NBA Draft Lottery
An emotional Hamilton told of how Harry's illness had affected him as he prepared for Sunday's Grand Prix. "I got some good points, every single point is going to count this year, so that's good for sure but I'm just keen to find out why the start was so bad".
Neither Ferrari driver was able to get onto the front row, which will be a fourth lock-out for the Mercedes-AMG Motorsport team in five races, with Leclerc's chances of threatening for a spot amongst the top four hindered by damage to his bargeboard, which came as a result of running wide at turn nine.
The Dutchman is now third in the title race, 46 points behind Hamilton. At the moment, I'm just enjoying driving with this team.
On their justgiving page, his family wrote: "We would like to say Harry will die in peace and comfort; to an extent he will, dying at home in his own bed surrounded by his toys and the people he loves". I was looking for inspiration and something to grab to so I dedicate today's race to him. I hope he's watching.More news: Maryland joins multi-state lawsuit alleging generic drug price fixing
"Then on the other side, if I take myself out from my Mercedes standpoint and all of the group, of course as a fan you want variability and unpredictability".
"No, naturally in negotiations - Toto's a very intelligent man so we have great negotiations and great conversations and naturally I've been with Mercedes since I was 13, so it's very hard to see myself anywhere else".
"You try to go out there to do something for someone but it doesn't always work out as it has".
Harry's father, James Shaw, said: "I don't know Lewis, but I think what we've seen is what a genuine, decent, lovely person he is".More news: Mandy Moore's This Is Us gets 3 more seasons