But La Liga have given a boost to Barca's hopes of keeping Messi by announcing that the release clause in his contract, set at 700 million euros ($833 million), still applies.
Messi and his lawyers believe a separate clause means he should be allowed to leave for free this summer.
Without passing a coronavirus test, Messi will be unable to join team-mates for Ronald Koeman's first training session on Monday, with the start of the new La Liga season less than two weeks away.
Messi was due for testing at 10.15am on Sunday but according to sources at Barcelona, he failed to show up at the Ciutat Esportiva.
The club's captain and greatest ever player could now be punished with a fine and even a reduction in salary if the strike continues.
Suarez, Vidal present
Luis Suarez – his best friend and strike partner – and Arturo Vidal were among those seen arriving for tests, despite both players being told they should find new teams as part of a planned clear-out this summer.
The meet-up was a chance for Messi to make his first public appearance since the burofax stating his intention to leave arrived in the offices of Camp Nou on Tuesday evening.
Instead, his absence offers a clear indication of his determination to secure a move and how ugly this dispute could now become.
Taking part in the team's pre-season programme could damage his legal case if his departure ends up being settled in court.
Barcelona insist a clause included in Messi's contract that allowed him to go for free this summer had to be activated by June 10 and the only way the 33-year-old will be allowed to depart now is via the payment of 700 million euros.
La Liga, who were always likely to take the side of the club, agree that Messi's release clause is still valid.
“The contract is currently in force and has a 'termination clause' applicable if Lionel Andres Messi decides to activate the early unilateral termination of the contract,” La Liga said in a statement.
“In compliance with the regulations and procedure in these cases, La Liga will not de-register the player from the (Spanish football) federation unless they have previously paid the amount of said clause.”
Yet Messi's lawyers believe the clause that allows him to leave for free refers not to a specific date but to 10 days after the end of the season. Given last season was extended into August due to the pandemic, with the
Champions League final only played last weekend, they maintain Messi's request to leave came within the agreed period.
His absence on Sunday suggests he is prepared to do whatever it takes to quit the club he joined as 13-year-old boy, and where most expected him to continue all the way through to retirement.
Supporters still hoping
Supporters, some of whom stormed Camp Nou in protest last week, remain hopeful Messi might still be persuaded.
Outside the training ground on Sunday morning, a young boy wearing a Messi shirt sat with his head in his hands, hoping his hero could yet return.
Mundo Deportivo, the Barcelona daily with close links to the board, wrote on Saturday how the club is defiant, even if every stance now could be a negotiating ploy.
“The more the days go by, the firmer the board and president Josep Maria Bartomeu are in not moving from their position,” it read. “Which is not to sell and, if possible, to renew the contract of Messi.”
Bartomeu made it known through the Spanish press on Thursday that he would resign if Messi said publicly that he was the problem and agreed to change his mind.
But Messi has remained steadfast. His snub on Sunday comes after he asked for a meeting, not to negotiate, but to begin facilitating an amicable and dignified departure.
Manchester City remain favourites to sign the 33-year-old, whose basic salary alone amounts to around 60 million euros.
If Barcelona and Messi decide to avoid a lengthy legal process, a compromise selling price of around 100 million euros could be within reach for City, while eliminating their less wealthy rivals.
Messi has reportedly spoken to City coach Pep Guardiola already but others remain in the running, including Paris Saint-Germain, Inter Milan and Juventus.