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Messi marked the end of his Barcelona career with an emotional press conference on Sunday after the Spanish club were unable to sign him to a new deal.
The 34-year-old Argentine superstar wanted to remain at the Camp Nou and was ready to take a staggering 50 per cent pay cut in a new Barcelona contract.
However, La Liga's financial regulations scuppered Barcelona's hopes of keeping Messi at the club.
Messi is now on the verge of a sensational free transfer to Paris Saint-Germain and is expected to fly out to Paris on Tuesday to finalise his move.
Koeman has insisted that he is "excited" about the upcoming La Liga season, despite losing former Barcelona captain Messi.
The 58-year-old Dutchman added that Griezmann could help fill the void left behind by the six-time Ballon d'Or winner.
"Despite the farewell to Leo Messi, we are very excited about this new season," Koeman said.
"With the squad we have, the signings we have made and also young people have come up, which is always the future of this great club.
"We are convinced that we will give you many joys this season. With a lot of help, a lot of sacrifice and a very good job we will achieve the maximum. We know what it is to be from Barca and what this club represents.
"It is important to have the best, but we don't change our ideas or the way we play either. Griezmann has played in his position and he has done well."
Griezmann arrived at the Camp Nou from Atletico Madrid in 2019 after Barcelona triggered his £107m buyout clause.
The 30-year-old French forward has previously been criticised for not replicating his Atletico form at Barcelona.
Griezmann, who was linked with a move away from Barcelona this summer, scored 20 times and registered 13 assists in 51 appearances across all competitions last season.
The former Atletico star was reportedly booed by furious Barcelona fans when he turned up for training last week.
According to reports, Barcelona were prepared to axe Griezmann this summer in a bid to reduce their wage bill.
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