Based on IRC (International Residential Code) and NFPA 31 (National Fire Protection Association) the only limitation for indoor oil tanks installation in a vicinity of fuel burning appliances is:
A paragraph from 2009 IRC (same as 2012 IRC and NFPA 31 requirements)
M2201.2.1 Tanks within buildings. Supply tanks for use inside of buildings shall be of such size and shape to permit installation and removal from dwellings as whole units. Supply tanks larger than 10 gallons (38 L) shall be placed not less than 5 feet (1524 mm) from any fire or flame either within or external to any fuel-burning appliance.
You have to remember to provide sufficient amount of combustion air for fuel burning appliances to support clean burning process and I would highly recommend (unfortunately not required in some jurisdictions) installation of a Carbon Monoxide alarm, or verify the location, age, and functionality of the existing one.