Speaking to the Scarborough Evening News, Burnham said the Government did not have the funds for a financial package to assist regional publishers, as was the case with several high street banks and car manufacturers.
However, he hinted the Government is open to preparing other measures to help the sector.
Last week, Daily Mail & General Trust (DMGT) announced it is to cut 1,000 jobs across its regional arm, Northcliffe Media, this year, double the number announced in November.
Burnham said: "One issue that has been raised is whether the government can increase adspend towards papers, instead of billboards or bus stops. It's a valid point."
Faced with plunging ad revenues and hundreds of redundancies, the regional media industry has lobbied the Government to examine various options for support.
In response, a number of reviews and initiatives have been kick started, including an Office of Fair Trading probe into local media ownership rules, which could encourage what many in the industry believe is much-needed consolidation.
In addition, the Society of Editors has written to Burnham detailing how the Government should help the beleaguered local newspaper industry. Meanwhile, the House of Commons Culture, Media and Sport Committee yesterday (26 March), launched an inquiry into the future of local media.
Burnham insisted that the problems facing the regional sector were "top of my in-tray", referring to concerns that some local councils are producing newspapers that compete with the regional media sector.
He said he would consider asking the Local Government Association to develop guidelines for local councils to police their activities.
He told the paper: "On the issue of local councils, it is, firstly, about what they are doing and are they encroaching? And secondly, could councils play an enabling role?"
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