It follows a seemingly surprising move made by Alonso's manager, Luis Garcia Abad, over the course of the Hungarian Grand Prix weekend towards Christian Horner, the Red Bull team principal.
The suggestions are Abad simply chatted with Horner with regard to a possible rising star on his books in Carlos Sainz Jnr who tested for Red Bull in the young driver test at Silverstone on July 19.
The rumour, however, is the two also discussed Alonso who is believed to be becoming increasingly frustrated with Ferrari's failure to provide him with a winning car.
Domenicali, though, has insisted Alonso should put more effort into helping Ferrari emerge from their current predicament.
Asked if he feared losing Alonso, Domenicali replied: "No."
He then added: "First of all we have a contract with him. For sure, Fernando is an asset to the team.
"We need him to work very closely with everyone because after all this is a difficult moment in the season.
"It's about team work. We have to deliver a job. Full stop. This is the same for everyone, not only for him."
The move appears highly unlikely given Alonso has another three years on his Ferrari contract beyond this one and it would cost Red Bull a fortune to recruit him.
Horner, however, did not deny being interested in Alonso, despite recently suggesting Webber's replacement had become a two-horse race between Lotus' Kimi Raikkonen and Daniel Ricciardo at Toro Rosso.
"We're in a fortunate position where there is quite a lot of interest in the seat for next year," said Horner.
"We'll look to make the right decision to ensure we have the right driver alongside Sebastian for next year."
Suggested to Horner it was not a denial, he added: "Any conversations with other drivers or other parties are always going to remain confidential.
"There have been quite a few drivers who have expressed an interest in the seat, as you can imagine."
Pressed again, and asked whether Alonso is an option, he said: "Is he available? I don't know. You ask him.
"We've some great options. We don't need to be in a rush.
"You always want to put the strongest drivers in your cars that you possibly can. Mark leaves some big shoes to be filled."
It is more than likely there is some gamesmanship going on behind the scenes, with Red Bull open to talks with Alonso as a potential way of pushing Raikkonen to make a decision.
Conversely, Abad and Alonso may be using Red Bull to urge Ferrari to buck up their ideas.
Alonso on Sunday claimed to be "very happy" at Ferrari, but then in the same sentence highlighted the problems.
He added: "Obviously we need to improve the car, and then we are going to have chances to win the world championship."
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