Airbus A319/20/21/30
see FCOM 2.1.30 - it's allowable subject to a couple of conditions
In the UK your company should have carried out a risk assessment in accordance with (I think) HSE guidelines and a CAA CAP (can't remember which one - sorry) that specify minimum distances from the refuelling point or fuel vents - the 'fuelling zone'; 6 metres rings a bell, but your company can, of course, choose a bigger distance. As long as your APU and its exhaust are outside that then no problems. You should have it published somewhere - if not, ask. As stated above, it's possible that there may be local regulations in force or restrictions for other aircraft types...