When a new client is trying to get a new IP from the DHCP server, it broadcasts the discover message. And also DHCP broadcasts the offer. And they use the transaction ID to communicate without the IP address. Would it be possible for another client in the same network to send a DHCP request with the same transaction ID to block the other client from getting an IP address?
Transaction ID are being chosen by client, so if someone wants to get the IP of the client, he only needs to spoof mac address associated with the entry in DHCP server.
If however, a client is already being assigned an IP by DHCP server, and the time lease is not yet expired, then by executing MiTM attack, and catching DHCP discover packet, it is possible to forge a DHCP packet with xid of a spoofed user.
Sorry, I didn't understood the question correctly. "Blocking" a user from getting an IP address is an entirely different process. And yes, it can be done.