The Spaniard had previously told the media in the homeland that he was expecting to sign a new deal with the club as he was quizzed about reports linking him with move to Real Madrid and Barcelona and it appears that he has been true to his word.
Indeed, 'ESPN' claims that the official announcement of the deal could be made as early as Wednesday.
As well as tying Alonso to the club for the next five years, the contract is also expected to include a significant improvement in terms of wages for the former Bolton man, who has successfully established himself as one of the best left-sided defenders in world football since joining the 'Blues' from Fiorentina back in August 2016.
Chelsea turned heads when opting to spend £24m on the buccaneering defender two years ago, but a string of impressive performances both in a back five and back four since have secured his place among the best defenders in the world.
The aforementioned source reports that several European heavyweights expressed an interest in the 27-year-old in the summer, but once it became clear that he was an important part of new boss Maurizio Sarri's plans attempts were quickly made to tie him down to a new deal.
"Alonso, at the moment, in this position at left-back is maybe the best in Europe," Sarri enthused back in September. "[His] physical qualities are at a top level, I think. He's doing very well in the offensive phase. But I also think he can improve in the defensive phase. If he improves that, he could be the best left-back in the world."
The former Real Madrid and Sunderland man has made 11 appearances for Chelsea in all competitions so far this season, being ever-present in the Premier League as he started the season with an impressive four assists and a goal in his first four games of the season.