The 23-year-old suffered an ankle injury on international duty with England back in May, but joined his colleagues in an open session at Anfield earlier this week.
"Daniel has looked really sharp and it's great to see him back training again," Downing told the Liverpool Echo. "Daniel is going to be very important for us. Hopefully he can get some minutes against Celtic and then be ready for the Stoke game.
"It's a big plus for us to have him back fit before the start of the season. The gaffer brought him in at a good time. We needed an injection of goals and he provided that.
"He settled in very quickly and I think he really enjoyed playing every week after being on the fringes down at Chelsea.
"He's got great ability, pace and strength; he causes defenders a lot of problems and if he carries on where he left off last season we'll be delighted."
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