Last Saturday, the left-back played the full 90 minutes as the Blues succumbed to a 4-1 defeat to Bayern Munich in the Champions League.
However, his appearance was not enough to convince Lampard that the Italy international has a future at Stamford Bridge, even as deputy to Marcos Alonso.
According to Football Insider, Chelsea value Palmieri in the region of £18m, rather than at the previously-suggested fee of £25m.
The report suggests that the Premier League outfit are hopeful that their asking price will entice Inter Milan into stepping up their interest in the 26-year-old.
Palmieri made a total of just 20 outings in all competitions during the most recent campaign.