The veteran midfielder has been locked in talks with the Capital club and has been training at Riccarton with the squad, with The Sun reporting the former Aston Villa man could be added to the Tynecastle squad ahead of Friday night's Betfred Cup clash with Motherwell at Fir Park.
Levein added former Cardiff midfielder Loic Damour last week while Manchester United goalkeeper Joel Pereira arrived on a season-long loan from the Red Devils earlier this week. The 23-year-old Portuguese youth international will be named in the matchday squad for Friday's cup tie provided international clearance is received in time.
His arrival could also prompt the departure of current No.1 Zdenek Zlamal before the transfer window closes.
Manchester City youngster Ryotaro Meshino - who only joined the Citizens from Japanese side Gamba Osaka earlier this summer - is also on the club's radar and was in the stands for the 0-0 draw with Ross County at the weekend.
Jambos assistant boss Austin MacPhee is fluent in Japanese after spending three years with FC Kariya during his playing career and this is understood to be a driving factor in Meshino's decision. Hearts are reportedly confident that the 21-year-old would be granted a work permit allowing him to sign on loan.