Bale has not played since injuring his calf against Villarreal on January 3 but the Welshman has resumed light training this week.
“Toni Kroos, Marcos Llorente, Mariano Diaz, Marco Asensio and Gareth Bale are close to coming back, Keylor Navas too,” Solari said at a press conference on Wednesday.
“They are all important players for the squad so we are happy.”
Madrid play Girona on Thursday in the first leg of the Copa del Rey quarter-finals before facing Espanyol in La Liga on Sunday.
Solari will hope to have Bale at full fitness again for the city derby against Atletico Madrid on February 9, with a Champions League tie against Ajax to come four days later.
Real delivered one of the best performances of the season to beat Sevilla last weekend, a result that moved them up to third in the table. They remain, however, 10 points behind leaders Barcelona.
Solari has not been afraid to leave out key players in a bid to improve the team’s form. Isco is yet to start a league game under the Argentinian while Marcelo has been dropped for the last two.
Asked if he had spoken to Marcelo, Solari said: “If I have had talks, they are in private. Competition is essential, they all know they can lose their place.
“Marcelo’s love for the club, his commitment to training and his behaviour are impeccable. Then it is up to me to pick the team.”