Suarez, who is banned from competitive matches until October 25 for biting Italy's Giorgio Chiellini during the World Cup, trained with Barcelona on Sunday ahead of Monday's Joan Gamper Trophy, the traditional curtain-raiser to Barca's season, against Mexican side Leon.
"The impression is that he is a player of a very high standard," Enrique told a news conference after Sunday's training.
"I know how we play and he fits how we play. I would like him to be able to play for a few minutes tomorrow.
"Not many, because he has not played for some time, but he has worked very well when training on his own."
Barcelona bought Suarez for £75 million from Liverpool last month.
On Thursday, the Court of Arbitration for Sport relaxed his ban, allowing him to train and play in unofficial matches, but upheld his four-month exclusion from competitive games and his nine-match international suspension.
Suarez will be available to play in competitive matches from Saturday, October 25, meaning his official debut could come in the first Clasico of the Spanish league campaign against Real Madrid.
Enrique, a former Barcelona player who replaced Gerard Martino after he stepped down at the end of last season following a trophyless campaign, insisted on Sunday Suarez's absence at the start of the season "does not harm us at all".
"The squad is solid and strong enough to face the first matches of the league."
Suarez bit Chiellini on June 24 in a 1-0 win over Italy. It was the third time in his career he had been found guilty of biting an opponent.
After his first training session with Barcelona on Friday, Suarez told the club website: "I'm paying for a mistake I made and one I have apologised for, but I have to forget about all this."
You can watch Barcelona take on Leon tonight on Sky Sports 5HD at 7.30pm.