[frenchie71]

Actually yes, because the nano does have an integrated UART (ch340 or ftdi etc...).
The esp8266 will be connected directly to the Tx/Rx lines. Moreover, ESP8266 has 3.3V and the 433MHz Module uses 5 Volts. This is the reason I used a 5V Arduino and "blocked" the 5 Volts using a !N4148 diode on Rx/Tx.

Now if you connect Rx/Tx to the nano I have seen weird effects due to the connected UART - in fact the ESP8266 might not be able to drive enough current "against" the UART - I am sure that electronically there might be a way around this but using a mini (which is the same thing, just no UART) is the easy way round...

Alternatively, just using an Atmel 328 Chip with minimal wiring might be an option as well...