Chelsea signed no players during the January transfer window, despite having their transfer ban lifted.
Although, the west London club did announce the signing of Hakim Ziyech from Ajax on a pre-contract agreement that will see him join in June.
Tammy Abraham has been the star man up top for the Blues this season, but Lampard was thought to be wanting quality competition and support for the England international.
The Frenchman scored in Chelsea's win over London rivals Tottenham Hotspur on Saturday to keep his hopes of a Euro 2020 spot alive.
Icardi is currently on loan at PSG, and it's a possibility that the French club will opt to make the move permanent.
However, the report states it could be a 'fiery summer' due to the interest surrounding the player.
It's reported that Real Madrid are also keeping an eye on the situation as they begin to plan for life after Karim Benzema.
