The 24-year-old is only a couple of days into a break having played a key role in Uruguay's Copa America victory over Paraguay on Sunday.
Dalglish has told the livewire forward, voted most valuable player at the South American tournament, he is not expected back at Melwood for a fortnight.
That would leave only a few days before the new Premier League season kicks off.
The Reds boss hopes Suarez will be "ready to compete" when he returns but will make a decision on whether the £22.8million January signing can feature at home to Sunderland on August 13 once he is back on Merseyside.
"It was fantastic what he achieved in the Copa America," said Dalglish.
"His performances were top-drawer and as well as individual accolades Uruguay won the tournament.
"He continued in the way he left us. He's made a fantastic contribution since he came in in January and I'm sure he'll be looking forward to the start of the season, especially after winning the Copa America.
"We're looking forward to getting him back. He'll have a good break now and hopefully we'll get him back in a couple of weeks, see how he is then and take it from there.
"We won't rush him. It's important players get the rest.
"It's important that he's ready to compete when he comes back. "Because he's been playing deep into July he's only getting a couple of weeks off but I'm sure it won't take much to get him fit or sharp.
"But we'll see how he is when he comes back and let him enjoy his holiday."
Suarez had the benefit of a long spell on the sidelines around the turn of the year when he served a seven-match suspension in Holland for biting an opponent while still playing for Ajax.
That may work in his favour when it comes to recovering quickly from his Copa America exertions.
One South American who should be available for the season opener is Lucas Leiva, who is due back in training next week after Brazil's earlier-than-expected exit from the tournament at the quarter-final stage.
Last season's player of the year will find added competition for places on his return to Melwood, with the club having signed midfielders Jordan Henderson and Charlie Adam.
Dalglish will look to get the 24-year-old back up to speed as quickly as possible.
"Lucas will be in next week and we'll see how he shapes up," the manager told liverpoolfc.tv.
"Obviously his tournament didn't go as well as Luis's did but he was fantastic for us last season.
"We're looking forward to getting him back as well and he should be well rested."