Plumbing inside of a house is often connected, so hearing water in a sink while the washing machine is running could be a sign that the washing machine is backed up or that the water line to your washing machine is connected to the water line going to your sink.
If a washing machine is backed up, toilets and sinks connected nearby will often provide the first sign. There will be a gurgling sound or slightly dirty water coming up through the drain. This can often be solved simply by unclogging the drain pipe on the washing machine. To do this, insert a long wire or cleaning snake in the disconnected drain pipe or hose to push out any material that may be clogging it. If the drain pipe or hose can be completely disconnected, run water through it with an outdoor hose or in the sink. It is also possible that the washing machine is simply pulling water through a pipe close to the sink, so that pressure is pushing some water up near the sink or faucet. As long as their is no major backup or water filling up the sink, this is not a problem. If it continues to be a nuisance, a local plumber can route the washing machine's water line away from the sink.