Short answer is not really, but http://www.percona.com/blog/2012/12/28/auditing-login-attempts-in-mysql/

Unfortunately, I don't believe there is a way to log authorization attempts to a separate file. Though if you set log-warnings = 2 in the [mysqld] section of /etc/mysql/my.cnf you'll get failed login attempts logged in the error log. From the docs:

If the value is greater than 1, aborted connections are written to the error log, and access-denied errors for new connection attempts are written.