Hearts are facing questions over the safety of their new main stand at Tynecastle after problems which led to delayed kick-offs at recent matches.
Police Scotland have written to Edinburgh City Council's public safety department over "significant concerns".
Kick-off was delayed for their first match back against Partick Thistle on 19 November over a turnstile issue.
A fire alarm triggered by a kitchen sensor caused another delay before last Saturday's game against Hamilton.
There were also problems with the floodlights during the 0-0 draw with Ross County on 25 November, caused by the electricity supply.
Hearts were given a temporary occupation certificate only on the morning of the Partick game after a last-ditch scramble to finish redevelopment work, which was originally scheduled to have been completed by early September.
The certificate has been re-issued on a match-by-match basis since, with the club confident a new one will be issued on Friday before Saturday's Premiership game against Motherwell.
Hearts are in the middle of a run of six home games in a row at Tynecastle, having played nine of their first 13 league games away from home because of the delays in redeveloping the main stand.
After the Motherwell match on Saturday, they are scheduled to host further games against Dundee on Tuesday, 12 December, and Celtic on Sunday, 17 December. They also face city rivals Hibernian at Tynecastle on 27 December.
Hearts issued a statement confirming they have been in contact with the Council over the "concerns regarding general security following a number of unrelated incidents at the first three games held at Tynecastle Park".
It concluded: "Following a satisfactory outcome to a meeting held today at the stadium, attended by all parties, the club is looking forward to welcoming Motherwell Football Club to Tynecastle Park this Saturday."
The letter from a senior Police Scotland officer to Edinburgh City Council includes concerns over increased risk of pitch incursions, crowd build-up and tension caused by the directors' box having "no delineation from the rest of the stand", lighting issues in different parts of the ground, and no water in certain sections.
"Given the incidents in the previous three matches, I now have significant concerns over the reliability of electrical systems within Tynecastle Park," the letter concludes.
"Electrical failings impact on public safety with evacuations and delayed kick-offs as evidenced in recent matches.
"This has an impact in the wider public space with persons queuing or being evacuated onto roads and the wider public space."
Police Scotland believe the likelihood of further emergency or evacuation procedures "to have increased significantly", forcing them to "re-categorise the risk associated with subsequent matches at a higher grade" and review the number of police and stewards.
They have requested the Council "re-examine the safety certificate" issued to Hearts for Tynecastle.
A spokesperson for the City of Edinburgh Council, said: "The safety of everyone attending matches is paramount and the Council is working with Hearts and their contractors to ensure that the matters raised by Police Scotland are addressed.
"As work in the stadium is ongoing, contingency measures are being put in place to reinforce safety procedures, while temporary occupation certificates and general safety certificates will continue to be issued on a match-by-match basis."
An SPFL statement added: "Hearts have undertaken to keep us up to date with developments and we will continue to monitor the situation closely."