Magnetic cooling has attracted considerable attention since it is an energy efficient and green thermal management technology. However, the cost of the magnetocaloric material, which is usually Gd based, has severely curtailed commercialization of this technology. Additionally, most commercial applications have service temperatures near room temperature. Hence, we studied the structural and magnetocaloric (MCE) properties of low cost Fe3-xMxAl (where M = Cr, Mn and x = 0.6 to 1) alloys with high relative cooling power (RCP) and Curie temperature (Tc) near room temperature. The Cr and Mn doped Fe3Al alloys exhibited either a L21 or B2 crystal structure. With increasing Cr content from x = 0.76 to x = 1, the Bohr magnetron per formula unit (µf.u.) decreased from 2.2 µB to 1.6 µB while coercivity remained low, no thermal hysteresis was observed. Among the Fe3-xCrxAl (x = 0.76, 0.84, 0.92 and 1) alloys studied, a maximum value of RCP of 300 Jkg-1 at 5 T and Tc of 300 K was exhibited by the Fe2.25Cr0.76Al alloy composition. A comparison of MCE based on the RCP/US$ performance metric suggested that these Fe3-xCrxAl alloys show higher RCP/$ values (~ 2.1) compared to other iron based and Gd based second order MCE materials (RCP/$ typically less than 1). In the case of Fe3-xMnxAl alloys, an RCP value of 425 Jkg-1 at 5 T and Tc = 260 K was observed for x = 0.6. For x = 0.7, Tc = 292 K and a RCP of 400 Jkg-1 at 5 T was observed. The RCP values of Fe3-xMnxAl alloys are comparable to those of the best known magnetocaloric materials. The low cost, high corrosion resistance, ready availability, good MCE values and established manufacturing technology makes Fe3-xMnxAl and Fe3-xCrxAl alloys attractive for near room temperature magnetic cooling applications.