The Real Madrid boss - who won two Premier League titles between 2004 and 2007 at Stamford Bridge - is widely thought to have agreed a comeback at the end of the season
The Real Madrid boss is widely expected to leave Santiago Bernabeu at the end of the season in favour of a second spell at the west London side.
Mourinho led Chelsea to a first-ever Premier League title during his first season in charge at the club in 2004-05, before retaining it the following term, and Lampard is keen for the Portuguese to return.
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"I've seen speculation before and a completely different manager walks through the door so we never know on that front but he is certainly one of the greatest managers, if not the greatest, in world football, so I'm sure the club and the fans will be happy to have him."
Goal understands that the Real Madrid boss will be unveiled in the Stamford Bridge hot seat in the coming weeks following a breakthrough in negotiations with the club.
Negotiations have centred on how much control Mourinho will have in recruiting players and staff, with the manager highlighting a desire to bring Radamel Falcao with him to Stamford Bridge.