Nico Rosberg's shock retirement from F1 - announced on Friday, just five days after winning the world title - has left Mercedes needing to find a new team-mate for Lewis Hamilton in 2017. With a seat available at the dominant team from the past three seasons, a number of drivers have been linked with a move.
Alonso is under contract at McLaren until the end of next season and new executive director Zak Brown does not fear the Spaniard could leave.
"We have a contract with Fernando and he is very happy," Brown told Sky Sports. "Obviously he wants to be winning races, as do we, but I am not worried about that scenario. We are very comfortable where we are at."
Former McLaren CEO Ron Dennis has made clear in the past that Alonso is locked in for the full three years of his contract, saying there are no performance-related clauses which could be triggered.
While Alonso is one of the most highly-rated drivers on the grid, Mercedes boss Toto Wolff this weekend stated it is not his intention to take a driver from another team.
Alonso is set to have a new team-mate in 2017, with Stoffel Vandoorne replacing Jenson Button, who effectively retired from racing in F1 at the end of this season.