Tigers host league leaders Gloucester Rugby (kick-off 6pm) with both sides boasting a record of three wins from three games at the start of the season.
Gloucester are two points clear at the top of the table thanks to bonus points gained in scoring 15 tries in wins over Leeds Carnegie, Saracens and Worcester Warriors.
Cockerill says Saturday will be a real test, especially as he has been assessing a number of injuries in a squad already reduced by Rugby World Cup calls.
?The players are to be congratulated on their efforts so far, but the challenges do not get any easier and we need to keep improving,? said acting head coach Cockerill.
?Those three wins will mean nothing when we run out against Gloucester. They have started the season extremely well and, on form, they will be favourites, which is unusual for us at Welford Road.
?This is a difficult part of the season for us and we need that famous Welford Road support right behind us, just like it was in the game against Bath two weeks ago. We enjoy fantastic support wherever we go and the guys always appreciate it. I am sure the crowd will get right behind the team again for another tough game.?
Supporters can watch two Rugby World Cup quarter-finals at Welford Road as gates will be open from 1pm. The match between England and Australia (kick-off 2pm) will be shown live on TV in the ABC, Tigers and Captains Bars. Food will also be available inside the ground from 1pm.
Then, after watching the showdown between the top two clubs in the Guinness Premiership, there will be live coverage of the second World Cup quarter-final between New Zealand and France, kicking off at 8pm.
Ticket are still on sale to see Tigers versus Gloucester, starting from £20 for adults, £18 concession and £8 junior (under-16). For more information or to purchase tickets, contact the Tigers ticket office on 08701 28 34 30.
On the turnstiles on Saturday, season ticket holders and members can pick up a voucher which entitles them and up to four guests to see the opening Guinness A League match of the season, against Leeds Carnegie on Monday, October 29, for free. To gain free entry as a guest, the back of the voucher must be completed in full.