Everton need to be sure of Steven Naismith's knee before signing the Rangers attacker.
The Liverpool Echo says the 25-year-old is believed to have visited the Blues' Finch Farm training ground on Saturday and completed an initial fitness test although he has yet to undergo a full medical.
Toffees medics wanted to determine how the former Rangers player's right knee has healed after he had surgery on it in November 2011 to repair anterior cruciate ligament damage.
So far the Blues have found no major issues and will push ahead with their bid to sign Naismith