The British pharmaceutical giant could sweeten its previous $13 per share offer for Human Genome with a small bump and a deal may come as soon as Monday, one of the sources said.

An agreement has yet to be reached and the talks could still fall apart, the sources cautioned. They asked not to be identified because the matter is not public.

Human Genome, which rejected GlaxoSmithKline's $2.6 billion offer in April as too low and launched an auction process, has come under pressure from investors to try and strike a deal with the British drugmaker in the absence of any alternative bids.

The U.S. company - an early pioneer of gene-based drug discovery - has set itself a July 16 deadline for finding higher bids, but interest has been limited because GSK, its long-time partner, already has marketing rights to its drugs.

U.S. biotech company Celgene Corp was at one stage considering whether to bid and conducting due diligence, according to a separate source familiar with the matter, but negative analyst and investor reaction when news of those discussions broke deterred the U.S. group.

Without alternative bids, Human Genome shareholders have been pressing the company's management to engage with GSK before July 16 to avoid a share price collapse - and that argument has been a trigger for the weekend discussions.

Human Genome, which has been trying to find another buyer in a separate auction process after GSK took its offer directly to shareholders, reached out first to its hostile suitor to negotiate a deal, according to one of the sources.

While the deal may get done at a small bump to the existing $2.6 billion offer, a so-called contingent value right (CVR) -- an additional benefit tied to a specific drug's success -- is not expected to be part of a deal, that source added.

A spokesman for GSK declined to comment, while officials at Human Genome were not immediately available.

Last year Human Genome and GSK won approval for Benlysta, the first new treatment for lupus in 50 years. But the drug's launch disappointed investors and Human Genome's shares fell from a high above $25 to a low of $6.51 in December. Glaxo made its offer a few months later, prompting Human Genome to launch an auction with the help of Credit Suisse and Goldman Sachs.

Human Genome and GSK share rights to Benlysta. They are also collaborating on two other experimental drugs in late-stage trials for heart disease and diabetes, where GSK owns a large majority of the economic interest.

Buying Human Genome would give GSK full rights to these partnered drugs, underscoring the appetite among big drugmakers for biotech products to drive future sales.

GSK would be also be able to strip out costs and the company's chief executive, Andrew Witty, told investors in May he expected to deliver "an extraordinary return" through the acquisition.

Human Genome investors have been hoping that GSK will sweeten its offer and the shares closed on Friday at $13.58 - above GSK's offer but well down on the level of more than $15 hit in April, soon after the unsolicited offer was made public.

There have been a spate of acquisitions of biotech companies this year as large pharmaceutical companies seek to rebuild their pipelines after a wave of patent expiries.

Most recently, Bristol-Myers Squibb agreed to buy diabetes specialist Amylin Pharmaceuticals by sharing the $7 billion cost of the deal with AstraZeneca.

(Reporting by Ben Hirschler in London and Soyoung Kim in New York; Editing by Susan Fenton and Gunna Dickson)

• A Permanent Economic Emergency