LONDON (Reuters) - U.S. General Electric (>> General Electric Company) is gearing up for a 3.5 billion pound ($5.3 billion) counterbid for British engineer Invensys (>> Invensys plc) that would trump last week's offer from France's Schneider Electric (>> SCHNEIDER ELECTRIC), a newspaper said on Sunday.

A bid battle between GE and Schneider, two of the world's biggest industrial companies, could drive up the offer price for Invensys to 550 pence a share, valuing the company at 3.6 billion pounds, Britain's The Sunday Times said, citing unnamed sources.

Invensys said on Friday Schneider was considering an offer of 505 pence a share in cash and stock, 15 percent above Invensys' closing price on Thursday.

The Sunday Times said its sources had cautioned that there was no certainty GE would enter the bid race, but shares in Invensys rallied to a ten year high on Friday on speculation Schneider's offer could flush out other bidders.

Invensys has long been mooted as a takeover target in an industry where larger rivals dominate.

U.S. group Emerson Electric (>> Emerson Electric Co.) was in talks to buy Invensys a year ago, while a report in May 2012 said Germany's Siemens (>> Siemens AG), Switzerland's ABB (>> ABB Ltd.) and GE had also made informal contact.

GE declined to comment. Invensys, which said on Friday it was likely to recommend an offer at 505 pence a share, also declined to comment.

(Reporting by Tommy Wilkes, editing by William Hardy)