With last season's top scorer Ben Burgess out until the new year with cruciate ligament damage, Taylor wants to add to his attacking options.
He told the Hull Daily Mail: "We've already strengthened our squad by signing Michael Keane and Leon Cort and bringing in a new striker is very much a priority now, especially with the situation regarding Ben in mind.
"We've looked at a number of players over the last few weeks and we've pretty much reduced the list to two.
"I've already spoken to a couple of managers and hopefully something will happen. One would cost us a fee and the other wouldn't but that's all I'm prepared to say at the moment."
He added that Iwan Roberts and Brian Deane are out of City's range.