It is understood the Magpies are hopeful of securing the 28-year-old Cameroon international on a Bosman free transfer as he approaches the end of his four-year deal at Stamford Bridge.
Geremi, who spent a season on loan at Middlesbrough from Real Madrid earlier in his career, made 23 starts and five substitute appearances for the Blues last season.
However, with Paulo Ferreira and Lassana Diarra competing for the right-back spot and Jose Mourinho boasting an embarrassment of riches in midfield, his future chances look limited.
Boro have repeatedly been linked with their former player this summer, although the Teessiders have insisted they have not been in the market for him.
Ironically, the right-back spot is one in which they have cover, although midfielder Nolberto Solano was used as an emergency defender in that position last season when Stephen Carr was either injured or having to play on the left.
However, Geremi's versatility could prove invaluable as Allardyce re-shapes his squad.
The manager has also been pursuing an interest in Marseille captain Habib Beye after releasing Titus Bramble, Craig Moore, Oguchi Onyewu and Olivier Bernard within days of his arrival at St James'.
Geremi's arrival would see him follow the same path as Damien Duff, who left Chelsea for Newcastle in a £5million switch last summer.