Mustwin351,
First the good news: from the player's point-of-view 3.7V is 3.7V, no problems there.
The bad news involves any "built-in" charging, this could prove to be problematic. There are several different lithium battery formulations with numerous different charging technologies associate with them, and they are NOT necessarily compatible. Some battery packs have a charge controller built-in, many use an external charge controller either built into the device's circuit or built into the charger itself. Without certain knowledge about the existing battery/charger you cannot proceed safely.
A Spot of good news. I assume the point is longer run-time AND that the MP3 player has a "charger" that connects to the player? If the connection is a standard mini-USB connector, or a standard wall-wort type connector, you can safely assume the MP3 Player's charge controller is either in the battery pack or in the MP3 Player's circuitry allowing you to use an "external" battery pack to extend the player's run-time. As long as the external battery pack's output voltage is within the MP3 Player's input voltage range, you will be fine.
Before going into more detail, you will need to provide information about the MP3 Player's charger, connectors etc. (AND, of course, if an "external battery pack" is an acceptable solution.)
Fish