No, telnet is not part of Apache.
What Distro are you using? Most Linux distros usually come with telnet already working.
The telnet daemon gets kicked by the inetd when someone hits the telnet port 23.
Look in the file /etc/services, there should be an entry for telnet:
This maps the port 23 to the word telnet. It is needed for the next file. Now look in the file /etc/inetd.conf and look for a line similar to:
#telnet stream tcp nowait root /usr/sbin/tcpd in.telnetd
If there is a comment (#) before the line, then uncomment it and if the line is missing, then add it. If you make changes to this file you will have to send a HUP signal to the inetd.
kill -HUP <PID of inetd>
Then try to telnet to your machine.
Let us know if this helps.