Henson's Osprey's contract expires at the end of this season and it was looking unlikely he would be granted his wish after Saracens, Wasps, Harlequins and London Irish all rejected the idea.
But he could be offered a reprieve by London Welsh with Taylor believing both club and player are a perfect fit - with the Championship club already having a player-sharing agreement with Ospreys.
"We're interested, very interested, providing he's interested," said Taylor. "We're not here to pander to Gavin in any way but I think he's a terrific talent.
"If he - as we all hope he does - gets his head right again and is really serious about playing good rugby again then we think there's a part in that process that we can help him.
"Our real interest is two-fold. If he is living in London then he would need somewhere to train - and even if he is good enough and committed enough to get back to where we would hope he is, he would need a number of games at a slightly lower level before he was ready to step back into top-flight rugby.
"I've spoken to Mike Cuddy and we are basically waiting for them to talk things out.
"They are in quite a difficult position and until that's sorted there's nothing that we can do to either move it forward or even just show that we're the place where he should be.
"We are hoping that we can help in the whole rehabilitation process.
"We are not anxious to sign Gavin as a long-term player for London Welsh because we know his aspirations are above that at the moment.
"What we think we can do is provide a very useful stepping stone both in training and in his first steps back on the playing field.
"Obviously we'd love to have him here, he would be a terrific draw down here at Old Deer Park.
"If he is in London, wants to stay in London and train in London then it could all work."