The Ireland full-back was released from the final year of his contract earlier this week, to spend more time caring for his seriously ill wife, who suffers from avascular necrosis, a crippling bone condition.
McNally, 28, helped Bradford earn promotion to the Championship, but is now expected to find a new club nearer his Leigh home.
Bulls host Halifax tomorrow in the reformed Yorkshire Cup and Kear is keeping his options open when it comes to making a move for another No 1.
“It’s something we’re discussing at the minute,” he said.
“We’ve got Brandon Pickersgill, who was fantastic last year when he virtually came from nowhere and established himself as a quality full-back.
“We’ve also got a youngster called Alix Stephenson, who I think a lot of, so we’re in two minds as to whether to go with what we’ve got or have a look and see if anything’s available.
“Players tend to come available after Easter, though, so we may well keep our powder dry until then. It’s open to debate.”
Eight clubs are taking part in the Yorkshire Cup – last held in 1992 – with Batley Bulldogs facing Halifax in the first part of an Odsal double-header tomorrow.
Dewsbury Rams host a double-header this afternoon when they face Featherstone Rovers after York City Knights tackle National Conference League champions Hunslet Parkside.
Semi-finals are next week before the Yorkshire Cup final on Sunday, January 20 as clubs attempt to make pre-season friendlies more meaningful.
The previous Yorkshire Cup ran from 1905 to 1992 before it was eventually disbanded.
Kear added: “It is good to do this as it gives us a certain amount of structure and jeopardy.
“But a trial game is a trial game; we’d love to win the Yorkshire Cup, but if it was that or beat Featherstone on the first day of the Championship season I’d sooner beat Featherstone.”
Kear will hand debuts to former Kiwi Test centre Jake Webster after his arrival from Castleford Tigers as well as Wales winger Rhys Evans and ex-Wakefield utility Matty Wildie.