Liverpool boss Brendan Rodgers has insisted Mario Balotelli will not be going out on loan in the January transfer window.
Switzerland defender Senderos, a summer signing by manager Paul Lambert, made his club debut in Villa's 1-0 win over Stoke City at the Britannia Stadium on Saturday.
He struck up an immediate rapport with fellow central defender Vlaar, the pair putting in an impressive defensive performance.
But after being one of Holland's stars during their World Cup run which saw them finish third, Vlaar has been widely touted as being a transfer target for several big-name clubs across Europe.
After Saturday's win, Senderos said: “It would be brilliant if he can stay. I think the club are trying everything they can to keep him and the fact he’s seen the team do well today he might think he should stay.
“He’s our captain and a very important player.”