Lampard's west London outfit have signed seven players this summer but continue to track a mega-money deal for the midfielder.
West Ham continue to demand around £60m for the 21-year-old.
But that isn't putting Chelsea off as they continue their mammoth spending spree in recent months.
The Athletic report Lampard is still keen on Rice and wants him to sit just in front of the back four at Stamford Bridge after Sunday's 2-0 defeat to Liverpool.
It is reported the Chelsea boss initially wanted to convert Rice into a central defender to offer cover for the likes of Kurt Zouma and Fikayo Tomori.
Rice could now sit at the base of the Blues defence should he arrive in the coming weeks.
Chelsea were beaten by Liverpool at the weekend after Andreas Christensen was shown a straight red card.
A Kepa Arrizabalaga howler also contributed to the loss - but Lampard backed his goalkeeper once again.
He said: "With the Kepa situation it’s a clear mistake. A clear mistake that has cost us because at that point we go on to have a penalty which we maybe score.
"Those fine margins change games at this level. He has to have support around him, that’s very clear.
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“It is clear now that there are two games where we have felt, today was a clear mistake and Brighton was a mistake too and he has reflected on it in that way.
“Players need support, particularly from myself. I give that to all the players. Kepa has to keep working, nobody tries to make mistakes in football, it is the nature of the game.
"You have to be strong, you keep going and that is where he is at.”