As you have already accepted an offer and started working there, it would be best to be straight with them and tell them what has happened if asked. To be totally honest I don't believe it will end in your favour however that is something you should of considered before accepting your previous job.
The new employer is likely to view this as indecisive and will be considering if you will simply hop to a new job if they give you this one.
If you lie, I think it would be reasonable to assume that it could come up at some point or they could ask you about it.
You will also have to consider any contractual notice period you may now have. If you still state you are unemployed they will assume that you can work right away.
On the other hand, if they don't bring it up, you don't need to tell them and it may not end up being an issue.