Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
McCormack arrives at Griffin Park on a free transfer from League One rivals Swindon while Saville will link up with the Bees on loan from Chelsea.
McCormack, 29, has signed a two-year contract and Brentford sporting director Mark Warburton told the club's official website: "We are delighted to see Alan join us here and he will undoubtedly have a positive impact both on and off the pitch.
"As captain of a strong Swindon Town team last season he clearly displayed excellent leadership and motivational skills and his experience will naturally benefit the development of the many young players we have in the first-team squad.
"Alan is a versatile player who will provide cover in a number of positions alongside his more recognised midfield role.
"We are looking forward to seeing him join us for the start of pre-season and to observing his performances in the season ahead."
Meanwhile, Saville has signed a loan deal until January. The 20-year-old has been a key member of the Premier League club's development squad and finished last season on loan at Millwall.