What model phones are they? Mitel IP Phones operating using a proprietary protocal called "MiNet", it is not compatible with Avaya equipment. That being said, many models of the Mitel phones are dual-mode and can be flashed with SIP firmware and run in SIP mode, assuming your Avaya can do SIP they should be able to work, although the amount of integration and feature availability may be limited.
You might be best off to sell them on eBay or through other channels and use the money to buy some refurbished Avaya phones.