The Spanish double world champion was ruled out of the opening race
in Australia by doctors treating him for the effects of a high speed crash.
Alonso has been training hard for his planned comeback at the Malaysian Grand Prix in nine days' time and used the McLaren simulator to hone his mental preparations.
The CNN-sponsored team announced the news on Twitter, showing McLaren sporting director Eric Boullier and Alonso at the team's headquarters in Woking, England.
Alonso was concussed and airlifted to hospital
after losing control of his McLaren at the penultimate winter test at Barcelona's Circuit de Catalunya on February 22.
The 33-year-old watched the Melbourne race from his home in Dubai after doctors indicated returning to racing three weeks after a high impact was too risky.
McLaren had explained that Alonso's "accident was caused by the unpredictably gusty winds at that part of the circuit at that time."
After getting back to race preparation in the simulator, McLaren tweeted that it had been a good day for Alonso, "focusing on operational work and practicing qualifying and race procedures."
The media enjoyed a guessing game in Australia about just how Alonso might have reacted to events in Melbourne, where Lewis Hamilton and his mighty Mercedes dominated while Alonso's McLaren teammate Jenson Button finished in last place.
Dane Kevin Magnussen, who was deputizing for the recuperating Spaniard, was unable to start the race because of engine problems on his way to the starting grid.
Alonso left Ferrari at the end of the 2014 season to rejoin McLaren, which is experiencing teething as it renews technical partnership with Japanese engine manufacturer Honda for 2015.
In his response on Twitter, Alonso chose to focus on congratulating Spanish rookie Carlos Sainz, who finished ninth on his Toro Rosso debut and who was inspired by Alonso as he plotted his own racing career.
"Congratulations to @carlosainz for the great weekend in Australia!! And of course to Hamilton and Mercedes for the win!! See you in Malaysia," Alonso's message read.
Meanwhile, Boullier is focused on finding improvements in the car's pace and performance for the next race on Sepang's sizzling circuit, which is also very physically demanding on the drivers.
"We know we have a mountain to climb as far as performance is concerned," the Frenchman said in a McLaren statement.
"In two weeks' time we'll be racing in Sepang [Malaysia], where the weather is bound to be extremely hot and humid.
"I'm not going to be rash enough to predict a form upswing in so short a time frame, but we'll be working flat out between now and then to make performance and reliability gains in any and every way we can, of that you may be 100 per cent certain."