It's not possible with the WebClient, I think.
What you could do is creating the WebClient by providing an HttpClient that has a connection handler set. When the handler is called, you can schedule checks for the given connection.
Something like this:
HttpClient httpClient = vertx.createHttpClient(httpClientOptions).connectionHandler(connection-> {
timerId = vertx.setPeriodic(period, l-> checkConnection(connection));
});
WebClient webClient = WebClient.wrap(httpClient, webClientOptions);
Don't forget to cancel the timer when the connection is closed (with closeHandler)