LaLiga clubs were on Monday able to train without restrictions on group size for the first time since the coronavirus pandemic led to the season being suspended in March.
The season will get back under way on June 11, with Madrid sitting two points adrift of leaders Barca with 11 games remaining.
Madrid's first game after the restart is against Eibar and Vazquez hopes it can be the start of a winning streak that enables Zinedine Zidane's men to claim a first league title since 2017.
"Eibar is the starting point for the 11 finals we have left and hopefully we can record wins in every game until the end and win the title," Vazquez told Real Madrid TV.
He added: "We like to train with all our team-mates together, enjoying the football.
"It's what we all like, training sessions in which we can all enjoy the football together. We're training to try and get into our stride for the start of the season.
"Football is made up of several factors, such as the physical side, which is very important, and the mental side. That combination of the two means that we can go into the league in good shape."
According to Marca, Madrid president Florentino Perez has informed club members they will play their remaining LaLiga games at the Estadio Alfredo Di Stefano at their Valdebebas training ground to enable renovation work to begin on the Santiago Bernabeu.