Lampard was unable to bring any new players to Stamford Bridge in his first transfer window in charge and has been frustrated at Chelsea’s failure to bring in recruits in January.
And according to ESPN, Lampard has identified Leicester City defender Chilwell and Ajax ace Ziyech as priority summer targets.
It is claimed Lampard is considering replacing title-winning left-back Marcos Alonso and wants to add more creativity to his midfield.
Chilwell, 23, has impressed for Leicester and England and has attracted attention from the Red Devils, among others, with Leicester thought to want £60million for the left-back.
United have also been linked with a move for £30million Morocco international Ziyech, along with Tottenham, but Lampard hopes Chelsea win the race to secure his signature along with Chilwell.
Speaking after Chelsea’s narrow FA Cup victory over Championship club Hull City, Lampard said: “We lost ground last summer [with the transfer ban] and we need to make moves now to take us forward.
“I have a strong feeling of where we can improve personnel-wise to take us forward. So for me it’s clear.
“The money of it is not my job but I have to be honest and truthful. Short-term recruitment is something we have to get right.”