I want to build a remote with Arduino Nano. I have viewed many tutorials in the web, but I don't have the IR Receiver (TSOP1740). Is there any way to use Jjust an IR Led as the receiver?
No, you can't use just an IR LED as the receiver. While it is true that an IR LED can also be an IR receiver the voltages it generates are really really small. So you would need an amplification circuit. On top of that the TSOP1740 includes a band-pass filter to isolate the carrier frequency of the transmitted signal from the background light, which you would also need to implement.
So yes, while you could use an IR LED as a receiver, you need a large amount of support circuitry with it (which takes expertise not relevant to this website) to get it to do anything useful.
You could make a remote without a receiver. It would require knowing what signals to send. The receiver is to essentially help in training your arduino by letting it detect the signal from an already working remote and then replay it on the LED.
You can't make a receiver with JUST an LED. (Majenko's got this one covered).