Spain international Alonso was heavily linked with a move away from Stamford Bridge during the summer transfer window, with Atletico Madrid keen to secure his signature.
The 28-year-old grew up in Madrid and spent almost a decade at Reals academy before moving to Bolton Wanderers in 2010.
The Blues legend has favoured Emerson in the left back position, with the Italian starting all four of Chelseas Premier League matches to date.
Chelsea had the opportunity to offload Alonso in July but blocked Atletico Madrids advances primarily because of the transfer ban that was looming over the Premier League club.
The Athletic also say that Chelsea prevented Alonso from leaving because they were preparing to appoint Lampard as manager and were unsure whether he would feature in his plans.
Lampard suffered a 4-0 defeat to Manchester United in his first competitive match as Chelsea boss before the Blues draw to Leicester City and beat Norwich.
They were held to a 2-2 draw in their final match before the international break and resume their Premier League campaign oRead More – Source