The 32-year-old was put through his paces for the first time since suffering a hamstring strain against Real Sociedad at the start of February and is close to making his comeback
The news comes as a welcome boost for Atleti who return to Champions League action on February 19 with a trip to San Siro for a last-16 tie against AC Milan.
Villa picked up in the injury in Atletico's 4-0 victory over Real Sociedad at the start of the month and returned to training on Thursday after missing almost two weeks of action, including the Copa del Rey semi-final defeat to Real Madrid and La Liga loss to Almeria.
The 32-year-old is seen as a vital part of Diego Simeone's plans, but the chances of him being rushed immediately back into the first team for this weekend's clash against Real Valladolid are slim and he is likely to start on the bench, according to reports in Spain.
Another first-team star, goalkeeper Thibaut Courtois, is still sidelined with back spasms and will not makes his return this weekend, while full-back Javier Manquillo is out after sustaining a neck injury against Madrid.
Third-placed Atletico will be hoping to put their slight dip in form behind them when they host Valladolid on Saturday.