The France international trained normally at Valdebebas on Tuesday and completed the session without apparent problems, giving Real Madrid a boost ahead of their return to domestic action.
Konaté withdrew from the France squad during the international break because of the injury but has now rejoined his club teammates. His return means he has a chance of being included in the squad to face Villarreal.
Éder Militão also took part in the session as he continues his recovery from injury. The Brazilian is progressing through his rehabilitation and could potentially be included in the squad, although his return would initially be about reconnecting with the group and rebuilding his match rhythm.
Real Madrid are therefore monitoring two defensive players ahead of the Villarreal match, with Konaté further along in his recovery after completing normal training.
Federico Valverde was absent from the club footage, meanwhile, after remaining in Madrid during the international break because of the ankle sprain he suffered in the derby.
The Uruguay international sustained the injury following a challenge from Lee Kang-in which was not punished by the referee and was not reviewed by VAR.
Valverde worked in the gym on Tuesday as Real Madrid continue to assess his condition. He has not been ruled out of the Villarreal fixture, but his availability will depend on his progress during the next few days.
The situation gives Real Madrid several fitness decisions to make before the return to La Liga. Konaté's return to full training is the clearest positive development, while Militão is edging closer to a return to competitive involvement.
For Militão, inclusion in the squad would represent another step in his recovery rather than an indication that he is ready for a full match.
Valverde, meanwhile, remains a doubt despite avoiding international travel and working at the club's facilities during the break.
Real Madrid face Villarreal on Saturday with the fitness of all three players still being monitored, but Konaté's return to normal training provides the clearest indication that he could be involved.