Already the best paid in F1, the Spaniard was earlier this week also hailed as "perhaps the best driver" on the grid by the Mercedes-Benz chairman, Dieter Zetsche.
Alonso's reply, given to Spanish reporters in Monaco on Wednesday, will only fuel rumours the 32-year-old is pushing for a change of teams, having failed to win a title in red and arguably losing his 'number 1' status in 2014 following the arrival of world champion Kimi Raikkonen.
When asked about Zetsche's praise, Alonso answered: "I don't know.
"It is always something good when good things are spoken about you, and the truth is that I am grateful.
"But it is interesting and it really seems curious to me that these types of things, this sort of praise, always comes from the other teams, from other people not from my own inner circle," Alonso is quoted by the Spanish sports newspaper AS.
The comment would seem to suggest a further souring in the relationship between Alonso and Ferrari.
Indeed, in Monaco, Alonso also denied that the arrival of new team boss Marco Mattiacci has so far had any impact on the struggling Maranello team.
And "I don't think it's going to happen soon," he told reporters.
"He's still learning about the team situation, the formula one environment, the F1 weekends," Alonso added.
"There is no change I feel in the qualifying, the races, the meetings, the work in the factory. Everything is as it was before."
Given Ferrari's situation, and Alonso's five-year wait for a title-winning car, the signs are that he has lost patience with the Italian team.
He does not expect Mercedes' dominance to be challenged this weekend.
"Monaco is a special track," Alonso is quoted by Marca newspaper, "so things could be a little different, but they have been first and second in every race with an advantage.
"We must not think that Mercedes will not dominate here," he insisted.