He is said to have retweeted his party's own exit poll before voting ended.
Bradford Council's returning officer made the report to police, according to BBC Radio Leeds.
Mr Galloway lost his seat to Labour candidate Naz Shah, who said his campaign "demeaned democracy".
It is against the law to discuss voting while polls are open, under section 66 of the Representation of the People's Act.
A spokesman for Mr Galloway told the BBC: "The returning officer is wasting police time. It's a storm in a thimble."
West Yorkshire Police said it would be reviewing the matter.
Mr Galloway snatched the traditionally held Labour seat in a by-election in 2012 with a majority of 10,140 votes.
It is not the first time he has hit the headlines over election laws - he was accused by Labour of making false statements about their candidate, Naseem Shah, in April.

The Italian, who won last month's Fifa elections to succeed Sepp Blatter, inaugurated the facility in the war-torn country's capital Juba.
He also attended the 2017 Africa Cup of Nations qualifier between South Sudan and Benin, which the away side won 2-1.
South Sudan played their first official friendly, against Uganda, in July 2012.
It was only in 2011 that organised football was first played in South Sudan, after the country gained its independence from Sudan.
South Sudan officials dressed Infantino in traditional robes and made him dance. Officials also produced a large cake to celebrate the Italian's 46th birthday.
After gaining independence from Sudan in 2011, South Sudan erupted into civil war in December 2013.
Infantino, who won last month's Fifa elections to succeed Sepp Blatter, is due to visit South American football confederation CONMEBOL from 28 to 29 March in Asuncion, the capital of Paraguay.

The London Taxi Company's (LTC) Ansty Park site in Coventry is the home of its new electric taxi, the TX5.
LTC - which now employs up to 1,500 people - has invested more than £300m in the TX5 after manufacturing the black cab in the UK for 69 years.
Administrators were called into LTC in 2012 before Chinese carmaker Geely bought the business the following year.
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The first electric taxis to roll off the production line will go on sale in London in the final quarter of the year, before being sold around the world early in 2018.
It has been described as one of the great comeback stories in UK manufacturing history - and that is exactly what it is.
Back in 2013 London Taxis International was on its knees and looking for a new owner.
Then Chinese firm Geely came to the rescue and almost immediately announced plans to build a new factory - but not only that, it revealed plans to make electric vehicles and employ more than 1,000 people.
It is the first all-new car factory in the Midlands since 2003, when Aston Martin opened its state-of-the-art plant at Gaydon in Warwickshire. That was on a much smaller scale, though.
It is also one of the biggest single Chinese investments in the region and it shows that the West Midlands continues to lead the way when it comes to both automotive research and development and production.
LTC, previously known as LTI, started life in the 1920s, producing car bodies for Jaguar, Rolls Royce and Bentley.
It will retain its existing Holyhead Road premises in Coventry as a paint shop once the production of the existing TX4 taxi ends in the summer.
Staff have moved into the Ansty Park plant this month ahead of Wednesday's official lunchtime opening, involving company representatives.
The new site will house a research and development centre for the electric vehicle, with engineers accounting for 200 of the newly-created jobs.
Respect leader George Galloway has been reported to police for allegedly breaking election law.
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South Sudan Football Association's new office was opened by new Fifa president Gianni Infantino on Wednesday.
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A £300m taxi manufacturing plant which created 1,000 new jobs is to be officially opened later.