Dzagoev has not played since leaving the pitch after 23 minutes with a hamstring injury during the tournament opener against Saudi Arabia last month.
The 28-year-old made the squad for their round of 16 match against Spain last week but was an unused substitute during their penalty shootout victory over the 2010 champions.
He then missed training on Wednesday with a back muscle injury.
"It was an old back injury. It was a bit jammed. Today I was training in a main group. Everything is fine. I am ready for the game," Dzagoev told reporters on Thursday at their training base on the outskirts of Moscow.
Earlier, Russia said the player had taken part in team training with some exercise restrictions.
The Russians have never reached the World Cup quarter-finals since the end of the Soviet Union, who were semi-finalists in 1966.
But the home team has so far exceeded expectations, coming out of their group with wins over Saudi Arabia and Egypt and defeat to Uruguay, before eliminating Spain in the last 16.
"As they say appetite comes when you eat," Dzagoev said. "Why not?," he said of his team's chances against favourites Croatia, perceived to be a dark horse in this tournament.
"(Coach) Stanislav Salamovich (Cherchesov) will tell us closer to the game how we are going to play. So far we have some draft ideas.
"We had fine games with Saudi Arabia and with Egypt as well as with Spain. Maybe we did not show our level with Uruguay but I hope we will manage to show our level against Croatia."
The winner of the tie will face either England or Sweden, who also play on Saturday, in the last four at Moscow's Luzhniki Stadium next week.
(Writing by Karolos Grohmann; Editing by Christian Radnedge)
