Police had earlier received complaints over Lennon's conduct during Hibs' victory over Rangers on Saturday but the former Celtic manager has denied any wrongdoing.

A force spokeswoman said: "Police Scotland is aware of offensive and threatening comments that have been posted on social media concerning a named individual and enquiries are ongoing in connection with this."

Police earlier confirmed they were making enquiries following the complaints about Lennon, which centred around his goal celebrations after Simon Murray made it 1-1.

The Northern Irishman cupped his ears and raised a fist towards Rangers fans, after being subjected to verbal abuse beforehand. Hibs went on to win 3-2 after Rangers midfielder Ryan Jack was sent off following a clash with Anthony Stokes.

Following the Ladbrokes Premiership match, Lennon insisted he had no concerns about his celebrations after the 20th-minute goal.

When it was suggested Rangers assistant manager Helder Baptista had spoken to police about him, Lennon said: "I didn't make a gesture, I celebrated a goal.

"If they are unhappy about it they can come and tell me. But I shouldn't get into trouble for doing that.

"I am celebrating a goal. What way are you supposed to celebrate a goal?"

Scottish Football Association compliance officer Tony McGlennan could also look into the incident.

Lennon has a two-game suspended ban hanging over him following a touchline clash with Morton boss Jim Duffy last season. The ban would be triggered if Lennon was found guilty of misconduct before the end of 2017.

Former Dundee United manager Mixu Paatelainen was handed a suspended two-match ban for similar celebrations, although more prolonged and aggressive, in front of Dundee fans in April 2016. An SFA disciplinary tribunal ruled he had breached rules by ''shouting and gesticulating at away supporters''.

Alex Smith, chairman of Scotland's League Managers Association, argued that there was a limit to the abuse a manager could take before responding.

The former St Mirren and Aberdeen boss told BBC Scotland: "I think the manager's got to be careful how he responds and how he handles that, because it can be volatile I suppose.

"Sometimes some kind of gesture can be misread and can be taken in the wrong context.

"That's when it becomes a bit dangerous, but I think if he's celebrating a goal and he thrusts his hands into the air and jumps around, he's entitled to do that.

"I've never known in my lifetime trouble in the terracing caused by managers in the dugout."

Former Celtic captain Stephen McManus also feels Lennon has a right to celebrate.

"Neil is a very passionate man, a very good manager," McManus said.

"I haven't seen the goals so I would be lying if I said knew what his reaction would be but I know how Neil used to celebrate any time a goal was scored wherever he played.

"He was happy the same as everyone else that's been involved in winning football matches, especially big games. You react in a way that makes you happy."

During his playing days, Lennon was the subject of death threats daubed on walls in Northern Ireland and on the road outside his home in Glasgow, and was sent bullets in the post while Celtic manager. In 2012, two men were each jailed for five years for sending letter bombs to Lennon and others.

The 46-year-old has also been the victim of assaults in the street and a Hearts fan was jailed for eight months for lunging at him on the sidelines of the pitch during a game against Celtic in 2011.