The 30-year-old was reported by team officials to be in danger of missing the whole tournament after he injured himself when attempting an overhead kick during training on June 4.
"We are not sure whether or not Kamil Glik will be fit to play in the first match but today he is going to take part in training," Nawalka told reporters on Monday.
"Kamil Glik is a very tough guy, he is doing everything he can to recover from his injury and he is training several hours a day, but whether or not Kamil will be part of the team against Senegal is unknown."
Nawalka has not decided whether Wojciech Szczesny or Lukasz Fabianski would start in goal, saying he would make the decision after training on Monday.
Overall, he said Poland had prepared "optimally" for the tournament.
"Our preparations began right after the draw was made and we have analysed both the strengths and weaknesses of the opponents," Nawalka said.
"We have prepared in an optimal way for our first games. Apart from the injury to Kamil Glik, nothing has happened to damage the harmony of our preparations."
His only concern seemed to be that a few members of the squad had not seen much action at club level.
"Some players unfortunately did not play a sufficient number of matches, but from the beginning we have tried to make sure it would not have any impact on their efficiency," Nawalka said.
He also paid tribute to Poland captain and record goalscorer Robert Lewandowski.
"Robert is an excellent captain as well as excellent player," he said. "His attitude is always very professional and I believe he can be viewed as an example by other players of how to run their career."
(Writing by Brian Homewood, editing by Ed Osmond)
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