The brokerage, which downgraded Human Genome stock to "market perform" from "outperform", said chances of the company attracting a better price were low as negotiations with Glaxo have become more "adversarial."
On Wednesday, Glaxo said it would proceed with its $2.6 billion offer only if the U.S. biotech firm removes a poison pill adopted on May 17.
"Human Genome's decision to enact a one-year shareholder rights plan suggests that a competitive process is unlikely to produce an alternate offer in the near term," BMO's Jim Birchenough said.
Glaxo and Human Genome together sell Benlysta, a new drug for the autoimmune condition known as lupus. They are also collaborating on two other experimental drugs for diabetes and heart disease, currently in late-stage trials, that could become significant sellers.
Birchenough said it would be hard for Glaxo or any other buyer to quote a higher price since a hike would have to be justified on the basis of a higher valuation for Human Genome's late-stage heart drug, and not the currently marketed lupus drug.
BMO's Birchenough, who cut his price target on Human Genome to $13 from $17, pointed to flat Benlysta sales trends as a reason for the limited upside to Glaxo's $13-per-share offer.
Glaxo chief Andrew Witty has already played down the possibility of increasing the offer price and said his company was the only obvious owner for Human Genome.
Human Genome shares, which have nearly doubled in value since GSK made its bid in April, were up 1 percent at $13.69 on Thursday on the Nasdaq.
(Reporting by Vidya P L Nathan in Bangalore; Editing by Sreejiraj Eluvangal)