The Uruguayan forward was a key player in his national team’s Copa America triumph this summer, scoring four goals, including one in the final against Paraguay.
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And Dalglish was full of praise for Suarez's performances in Argentina.
"It was fantastic what he achieved in the Copa America. His performances were top-drawer and, as well as individual accolades, Uruguay won the tournament."
His participation in the tournament means that Suarez, 24, is yet receive a rest ahead of the new season, something Dalglish is very mindful of.
"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."
Unlike his club team-mate, Lucas Leiva endured a difficult Copa America with Brazil. The midfielder was a regular fixture in the side that crashed out to Paraguay on penalties at the quarter-final stage.
Despite the tribulations Lucas endured, Dalglish found positives in the situation and welcomed the extended rest period the Brazilian will enjoy.
"Lucas will be in next week and we'll see how he shapes up. Obviously his tournament didn't go as well as Luis' 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."
