The Sunday Post reports that the Serie A side were eyeing up a move for the Hoops ace worth around £4.5 million, however, Stefan De Vrij signing a new deal at Stadio Olimpico has handed Lazio a boost.
De Vrij is wanted by Barcelona and Inter Milan, according to The Sunday Post, but he has extended his contract that was due to expire in the summer - and the new deal includes a release clause that will allow him to leave for £22 million.
With the Dutchman looking set to remain until the summer, The Sunday Post suggests that a move for Simunovic is unlikely during this month's window and the interest may be reignited at the end of the campaign.
With Erik Sviatchenko loaned out, it may feel like a boost for Brendan Rodgers that Lazio are planning to delay their pursuit of the 23-year-old. Simunovic may not have been at his best this season, but he is still a very promising centre-back and losing him in the final days of this window would have been a blow.
And of course, just because Lazio have shelved their plans for the time-being does not mean that Celtic will not have to contend with offers from elsewhere. But the fact that one of Europe's more high-profile clubs is seemingly not in the running right now may well give Rodgers a small reason for optimism.