Yes, but it is hard to see. The blue bar under the green menu at the top of the page will give you a status update saying someone placed a higher bid than yours. But, it only tells you on the first page you visit, so it is easy to miss.

The best thing to do is click on "Club" from the top menu, then "Bids" on the left hand nav. This will show the bidding status of any player you've placed a bid on until the bidding stops and that player is transferred.