Two large shareholders in G4S
The newspaper said the two shareholders, which own 2 percent and 1.35 percent of G4S's shares respectively, would join other investors which are also opposed to the deal, ahead of a November 2 shareholder meeting.
Since the offer was announced, G4S, which is the world's biggest security company, has faced a backlash from some shareholders which have objected to the strategy and financing behind the deal.
Shares in the group have lost almost 13 percent since it was announced -- partly due to the dilutive impact of a proposed 2 billion pounds rights issue to help fund the deal.
Shareholder Parvus Asset Management has led opposition to the takeover, calling it an untested vision that it would not support.
The Sunday Telegraph said Danish investors, which in total own around 10 percent of G4S, were also thought to be sceptical and the Abu Dhabi Investment Authority was set to abstain.
A spokesman for G4S declined to comment.
G4S has previously said it has received positive feedback from shareholders over the deal, which would enable the company to move into areas such as cleaning and catering.
(Reporting by Kate Holton; Editing by Helen Massy-Beresford)