Burns, who scored 13 goals in his first season with Phoenix, is out of contract and widely tipped to sign for an overseas club.
This scenario prompted Phoenix coach Ernie Merrick to step up his chase for a top striker to replace the former Adelaide United man who has revived his career after a mixed adventure in Europe and Asia.
"We are after a quality striker anyway," said Merrick, who led Melbourne Victory to two championships in 2007 and 2009.
"We need someone with a proven track record who is capable of performing under pressure and help youngsters develop.
"That's why I signed Joel Griffiths last season.
"We can't control what happens during the silly season. All I can do is prepare for any eventuality.
"There is a lot of player movement and if Nathan moves on, yes, we'll be looking more eagerly for another striker."
Merrick's recruitment policy at the start of last season came in for plenty of praise, particularly for attracting the prize signatures of star midfielders Michael McGlinchey and Roly Bonevacia.
He said he was not into buying big-name players merely to put bums on seats but he preferred dependable performers capable of fitting into the Phoenix mould.
"You've got to make sure you've done all your homework for recruiting," he explained.
"We follow certain criteria when buying players. We have a very specific profile for the striker that we want and if the player lives up to those criteria then our fans will love the fact that we've signed him.
"We've got a visa spot available so, yes, we are keen to fill it."
Phoenix at one stage last season was playing so strongly at home and away that it was seen as a genuine contender for the championship.
But the wheels fell off towards the end of the season and the club had to be content with fourth place on the ladder.
It also bombed out of the finals in the first week, losing 0-2 to Melbourne City.
Merrick said the reason for Phoenix's drop in form towards the end of the season was a lack of depth in the squad.
"I thought we had a good squad but we did not have enough depth, particularly up front," he said.
"That's why I signed Griffiths but when he got injured we had a problem."
Merrick said Burns's drop in scoring rate after coming back from the AFC Asian Cup in January was not the reason for Phoenix's failure to finish the season with a flourish.
"I think any player who scores the number of goals Nathan scored is doing his job," he said.
"Nathan was a key goalscorer for us and he was marked very tightly after the Asian Cup.
"That's why his goals dried up a bit after the tournament.
"I think our problem was there were not enough players stepping up to a higher level and taking the pressure off him.
"But all in all we scored 45 goals and that's a record for this club.
"I think it shows that we are on the right track."
