The Chilean boss had his departure from CSL outfit Hebei China Fortune confirmed on Saturday, and reportedly touched down in London to finalise a deal on the top job at West Ham.
The Hammers had been searching for a replacement for David Moyes, who left last week, and had narrowed their selection down to four candidates, of which Pellegrini is reportedly his confirmed successor.
Pellegrini has previous Premier League experience at Manchester City, having led them to Premier League glory in 2014, and to their first and only Champions League final in 2016.