You can refinance your conventional mortgage into a FHA mortgage. 

FHA will allow you to refinance to 96.5% loan to value but there can be no cash out.  Loan to value means the amount of your loan as a percentage to the value:  example value of home is $200K with a loan of $193K gives you a loan to value of 96.5%.

If you are trying to refinance an into an FHA loan and taking cash out than there are limitations.  Most banks will not allow you to take out cash beyond 85% loan to value.  What does that mean:  If your home is worth $200K you cannot have an FHA loan with cash out beyond $170K.

This is for loans that are $417K and under.  The guidelines for loan amounts > $417K to $729,750 maybe different. 

FHA has max loan amountsallowed that are based by state and than by county.  These limits are set by HUD.  The max loan limits are set by HUD and are 120% of the median home price for the county to a max loan amount of $729,750.  Example:  Calaveras County, CA max loan amount is $462,500 for a single family home versus in San Francisco County, CA the max loan amount for a single family home is $729,750 which is the max amount HUD will allow for FHA.