The Giants’ official, on-the-record position on Burress, as spoken through Reese, has never changed from the moment he was sent away to prison. They simply won’t publicly rule out a possible return. That doesn’t mean that they’re readying for his return or that’s the reason why they’ve yet to give out his old No. 17. Reese doesn’t rule anything out. He investigates everything. And he’d be crazy to rule out any player, not knowing what the future holds.

However, if you are for some reason holding out hope for a Burress return next season — if there is a next season — there are some other factors to consider. The biggest one may be that Giants officials, off the record, are much more leery of Burress II than Reese’s public stance would indicate. It’s not that they’re against second chances or feel that he’s somehow irredeemable. It’s about a host of other factors, including these:

– Ralph Vacchiano, N.Y. Daily News.

Vacchiano lists the reasons the Giants won’t and probably shouldn’t re-sign Plaxico Burress once he’s out of jail. They include: He’s old, he’s a distraction, he violated a bunch of team rules even before he shot himself, and they’re happy with their crew of young receivers.

That all seems to make sense. But I can see none of those things precluding the Jets from pursuing Burress this offseason, assuming the lockout eventually ends and any team ever pursues any player this offseason. Under Rex Ryan and Mike Tannenbaum, the Jets have frequently looked to find value from aging stars on short-term deals late in their careers.

Plus, they’ve welcomed players labeled distractions or reputed to have “character” issues — Braylon Edwards, Santonio Holmes, Antonio Cromartie, Joe McKnight — and mostly met with success.

Assuming the Jets will not have the funds to return both Edwards and Holmes, Burress might make a nice, big, inexpensive target for Mark Sanchez in the 2011 season. So I say do it.