I have J1-visa currently which will expire April 2009.

A place where I am being trained would like to hire me and change my visa to H1B.
Do I need to leave the country or not?

"J1 visa holders are required to reside in their home country for at least two years before they may obtain an H, L or other immigrant visa to enter the U.S. or adjust their status within the U.S."
So it appears that your employer's application for H1-B visa for you will not be approved.
You may have to go back to your country and get waiver for this "2 years residency" from your country. As far as I know, the U.S. can't waive this condition.