It's possible, but the club don't think it's financially viable at the minute - from the latest fans forum:

PF outlined that NUST has pushed for stadium expansion at the Gallowgate End for a long period of time.

PF advised that NUST had previously met with construction firm Tolent, which was involved in potential redevelopment of the Strawberry Place site. Tolent produced a report to show that the Gallowgate End could be cantilevered and extended to accommodate an additional 8,000 – 10,000 supporters.

PF stated that NUST would not make a business case for the redevelopment as they did not feel it would be viable, but they believe the club would want to have more supporters inside the stadium if it could.

LM highlighted the club’s comments from two consecutive Fans Forums in 2014, which indicated that extending the Gallowgate would not make sense commercially and that its view was likely to remain unchanged in the short and medium term and potentially the long term.

At that time, the club also stated that selling St. James’ Park to build a new stadium was not an attractive or realistic option.

SW asked if demand for tickets had changed since 2014. PF suggested that the size of television broadcasting deals could make financing stadium expansion easier. SH suggested that the club could keep expansion as a possibility rather than ruling it out, particularly with high demand for ticket.

The club reiterated its stance that outlaying what could potentially be tens of millions of pounds to expand would be unwise financially. The club stated that there is demand for tickets for ‘bigger’ games but that this is not always the case for other matches, when demand tails off.

The club highlighted Saturday’s match against West Bromwich Albion, which had originally sold out. The visitors returned a block of seats on Level 7 in advance, however those tickets were being sold in very small quantities each day, indicating that demand was not especially high.