Richardson – who played for the Dons in the early 90s and scored a memorable long-range effort in a European Cup Winners’ Cup tie against Torino in 1993 – is now a sports psychologist.
Klopp has recruited the 50-year-old to consult with the Liverpool squad, who are eight points clear at the top of the Premier League.
He has his own office at the club’s Melwood training complex and is based there three days a week.
Richardson, who turned out for Halifax, Watford, Blackburn Rovers, Oldham, Stockport, Huddersfield, Bury, Livingston and Chesterfield in a 17-year career, has also worked with Lancashire County Cricket Club and was previously part of the backroom staff at West Ham and Crystal Palace.
He spent two years managing Chesterfield between 2007 and 2009 after hanging up his boots.
Scottish football fans will most likely remember him as part of the Aberdeen squad that finished second behind Rangers in all three domestic competitions in the 1992/93 season.
Richardson netted in the Scottish Cup final, scoring a 77th minute goal as the Dons went down 2-1 to Rangers in a repeat of the Scottish League Cup final, in which he also featured.