Possibly, if it is leaking from the bottom only, and if you have a Domus Due model, you might just need a new water reservoir as the water reservoirs are a different system than all of the other briel machines and a new reservoir will usually fix the problem of leaking on the bottom in the Domus Due machines. Something with the seal on the reservoir.
You can order just a water reservoir by contacting the service center at:
41 Woodbine St
Bergenfield NJ 07621
If your machine is leaking over the filter handle, brew head etc, that could be the coffee oils have built up in the Brew Head Screen and/or filter basket itself. For that, remove the Brew Head Screen and soak along with the Filter Basket in a coffee oil remover (not descaler) you can get the Cafiza powder at www.urnex.com
or any other brand and then use a brush to clean it after soaking. If you have the Briel filter basket with a screw in the middle, please remove the screw and clean in there as it tends to get clogged. Then just be sure not to screw it too tight again as this can cause leaking.
I hope the info was helpful.