By ESPNSTAR.com staff
The 22-year-old impressed for Russia at Euro 2012 with three goals and is thought to be valued by CSKA at around £15million.
Dzagoev has long been touted as one of the best prospects in European football and he is out of contract at CSKA in December.
His father, Tariel Dzagoev, was quoted in The Sun: "I don't know if he will stay at CSKA. There are offers - from Spurs and other foreign clubs.
"But I tell him not to hurry. Yuri Zhirkov ran off to Chelsea and sat on the bench."
Arsenal and Chelsea were also rumoured to be interested in bringing the midfielder to the Premier League.
"Of course, I have the desire to try myself in other clubs in Europe," said Dzagoev prior to Russia's final group game against Greece.
The Russians were eliminated from Euro 2012 at the group stage by Greece thanks to a goal from Giorgos Karagounis which sealed a 1-0 win.
Spurs are not likely to be in any rush to sign Dzagoev as well considering that the club are still looking for a successor to Harry Redknapp. The former Portsmouth boss parted company with the north London club after almost four years in charge at White Hart Lane last month after failing to agree a new contract with chairman Daniel Levy.