Rodgers worked with Lampard at Chelsea and was delighted to see Sigurdsson win the Player of the Month award yesterday.
He said: "It's a great honour for Gylfi. The number of goals and his overall performance level have been outstanding.
"He has been a wonderful acquisition for the club. I knew what I was getting and he has delivered brilliantly. Let's hope he can keep it up until the end of the season. Gylfi's in the Frank Lampard mould. He's that type of goalscoring midfield player. Frank always wants to be better every single day - and Gylfi is the same."