You may have oil leaking from a number of points, you may have an oil pan leak on the backside, that could be burning off. You may have valve cover gaskets that need replacing. You may also have failing valve seats that where you would not have an obvious external leak and may be so slight that there is no smoke.
Internal oil loss can be caused by several things. I would start with checking the PCV (crankcase ventilation valve). If the PCV remains stuck open, it may allow excessive oil to be sucked into the engine and burned through the normal combustion process.
There may also be internal engine wear such as a valve seal or piston rings that are just not sealing how they should be. A compression test may indicate it there is an internal issue that needs to be addressed.
Also note that for many vehicles, burning a quart of oil in 3,000 miles may be considered normal.
〉 Answered on Jan 17th, 2015 by Helaine Kurot, Owner/Technician at 360 Automotive