Asked if a deal is "close" after weeks and months of speculation, team executive Zak Brown said this week: "We've been close for some time.
"We wanted to get the Asian races out of the way and our new power unit partner in place which is now done. I expect we'll have a positive conclusion to our plans with Fernando soon."
On Tuesday, the FIA announced that Alonso will appear in the official Thursday press conference in Austin, and Brown hinted that the Spaniard may have some news to share.
"He's in the FIA press conference on Thursday," Brown said. "We have to get a deal done before anything is announced."
It is not believed that McLaren and Alonso are in dispute over what is expected to be a huge €40m (£35.8m) deal for Alonso.
Rather, the sticking points could be contract duration, and whether Alonso will be free to race in other categories, as he did at the Indy 500 this year.
Brown confirmed that a new Alonso deal would include provisions for him to race elsewhere, decided "on a case by case basis".
However, he said that Le Mans might not be on the cards for 2018, because the current regulations would not accommodate McLaren's own GT3 or GT4 cars.
"Le Mans is something we're looking at," said Brown. "As a manufacturer we're participating in meetings.
"Le Mans is of interest but whatever rules they land on need to be a good platform."
Alonso has picked up 10 points for McLaren in 2017.