Chelsea have reportedly offered Olivier Giroud as part of a player-plus-cash deal to sign Lyon striker Moussa Dembele.
Giroud has been linked with a move to Italy, while other reports have suggested that the striker could make a return to France.
According to The Sun, Chelsea have approached Lyon with an offer of £40m plus Giroud in exchange for Dembele.
The latter, who is 23, netted 20 goals in all competitions during his debut campaign with Lyon last season and already has 10 Ligue 1 goals this term.
Lampard is keen to add attacking options to his roster this month in an attempt to ease the goalscoring pressure on Abraham.