According to Mundo Deportivo, the Paris Saint-Germain forward is keen to see the Ligue 1 giants sign Griezmann next summer to avoid his global team-mate moving to Old Trafford.
It was claimed Barca wanted Griezmann to play alongside Messi and form a partnership under Ernesto Valverde.
If he were to sign, Griezmann would replace the departed Neymar ahead of other attacking options available to Valverde, but leaving the Wanda Metropolitano would be a huge source of consternation in the Spanish capital.
Also, there have been some rumours that Griezmann himself has asked Mbappe to secure him a move to France as he has no intentions of staying at Atletico for another 12 months, given that the club have already signed Diego Costa from Chelsea.
Griezmann was heavily linked with a move to Manchester United but the French forward opted to remain at the Spanish club after Atletico were slapped with a Uefa transfer ban.
Day One testimony continues in Jessica Chambers murder trial
She has said she spoke to her daughter on the evening of December 6, 2014, and will likely testify about that night. He also said that Mr Tellis had repeatedly asked Chambers for sex, and she had told him no, according to Fox news.
Porsche reveals Cayman e-volution, 'Turbo' Charging System for EVs
Porsche's latest is an all-electric Cayman that can charge almost three-times faster than a Tesla Supercharger. And with the Turbo Charging name, Porsche can still put that lovely Turbo script on the back of cars.
Grab Verizon Moto Z2 For for just $450 on Best Buy
If you decide to go for Verizon's offer, you'll end up paying $456 for the Moto Z2 Force over the next two years. Users should remember that these are Diwali discounts and will only be applicable on offline purchase.
Lionel Messi and Antoine Griezmann, two of the three podium finishers in voting for last year's Ballon d'Or, have been named among the 30 nominees for the 2017 edition of the honour.
The 26-year-old almost joined Manchester United this summer.
Mourinho has told Red Devils chiefs to spend £88m (€100m) on the France star.
With that being done, Griezmann eventually chose to sign a new contract with the capital, until 2022, which saw his release clause hike to £178m, which all but scrapped United's hope of landing the Frenchman.