Elimby is part of the Blues Under-23s set-up and is now poised to make a move to their London rivals West Ham.
The 19-year-old has been on trial at the London Stadium in recent weeks and it appears West Ham are impressed with what they have seen from the midfielder.
According to French radio station RMC, West Ham are on the cusp of sealing a deal for Elimby, with €1.5m compensation agreed with the Blues.
Chelsea will also be in line to receive a profit from any future sale of Elimbny, as they have secured a sell-on clause amounting to a substantial percentage in the agreement.
Elimby was snapped up by Chelsea from the youth ranks of French outfit Nantes in the summer of 2018, and he is now set to leave Stamford Bridge after three years on the books.
West Ham are determined to strengthen their roots and are keen on adding up and coming talents to their academy, which Elimby is now set to join.
Elimby featured seven times for Chelsea in the Premier League 2 in the season gone by and will now have the opportunity to kick on with his development at the London Stadium.