Price per square foot is not a good indication of value of a property or values in any specific market area. There are too many variables and specifics of individual properties and the market area that need to be considered. The average price per square foot in an area is derived from ALL real estate transactions from ALL types of properties within the area, for a time period normally running around 2 to 5 years. Even if the data was filtered to a specific property type, and a specific time period, the different types of transactions would also need to be filtered to to arrive at vague estimate of price per square foot if that is what you want to base your offer on.
If you have a couple of properties you are interested in, and are considering an offer, it would be wiser to consult with an appraiser to help determine an offer price. Since a state licensed appraiser does not have a vested interest in the outcome (commissions), you would get an unbiased opinion. You would not necessarily need to order an appraisal, a consulting assignment would be more appropriate and would fall in line more with the appraised value, than an agents estimate, when your lender orders the appraisal.