Tuilagi missed the 19-18 Premiership win at Gloucester with a "hamstring tweak" just a fortnight after returning from a long-term groin injury.
He is unlikely to return until Tigers' trip to Newcastle on 12 February.
"Results normally polarise decision making," Cockerill said.
"It depends on how England go up at Murrayfield against Scotland next weekend really. They might not need him.
"If they don't get the result up there, then they might want him back sooner, rather than later."
Tuilagi was just three games into his comeback after 15 months out of the game - but new England head coach Eddie Jones is keen to bring back the 24-year-old, who has not played Test rugby since June 2014.
"He probably won't play next week [the Tigers' Premiership game against Sale] and will probably come into it for Newcastle the week after," Cockerill told BBC Radio Leicester.
"If he is playing and back fit, then it is up to Eddie. Manu's groin is great. Now it is a case of keeping the rest of his body intact as well.
"Fifteen months out of the game is a long time. We are trying to manage that and integrate him back in as sensibly as possible.
"His hamstring was a bit tight after the Stade Francais game last weekend. He had it scanned on Monday and there was the tiniest of strains there. It is nothing serious."

There were men's singles golds for Martin Rooke (WH2), Daniel Bethell (SL3) and Krysten Coombs (SS6) while Rachel Choong claimed women's SS6 singles gold.
Another three golds in mixed events followed, with three silvers and eight bronzes completing the total.
Para-badminton will make its Paralympic debut at the 2020 Games in Tokyo.
There were also three bronze medals for Scotland's Colin Leslie, Fiona Christie and Bobby Laing at the four-day event in Beek.
See the full results here.
Leicester Tigers boss Richard Cockerill says that England centre Manu Tuilagi's latest injury is "nothing serious" - and that he could still figure in this year's Six Nations.
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England's para-badminton team dominated at the European Championships by winning 18 medals in the Netherlands.