The Welsh All Blacks' 38-29 defeat to Amatori & Calvisano in Round 3 means they seem likely to bow out of the competition this week.
'We are travelling to Leicester playing for pride, as we have no realistic chance of qualification,' said head coach Lyn Jones.
'It is a long time since we have played at Welford Road as a club, so we are looking to enjoy the occasion and hopefully play some entertaining rugby.'
Neath almost surprised the double champions in Round 1 as they pushed for the victory, leading the match going into the final minutes before an audacious Austin Healy try gave Leicester a late lead.
But ill discipline from Tigers French prop Frank Tournaire in the final minute gave Wales A fly-half Lee Jarvis the chance to level the scores.
And Neath have picked a strong side that will, as ever, be captained by Wale international second row Gareth Llewellyn as they attempt to inflict the first home defeat on the Tigers in Europe in three season's.
'We have picked a strong side and travel to Welford road with the intention of winning the match. It is difficult to identify areas of weakness on the Leicester team, and the fact that they are twice European Cup winners says it all.
"There are areas where we feel they are less strong, and we have concentrated on these in training. I am hopeful our hard work show through with the right result on Saturday,' said assistant coach Rowland Phillips.
Leicester can secure a home spot in the quarter-finals if they can beat Neath.
Neath: A Durston; G Morris, A Bateman, D Tiueti, S Williams; L Jarvis, A Moore; P James, B Williams, A Jones, S Martin, G Llewellyn (capt), A Mocelutu, S Tandy, R Phillips
Replacements: S Jones, J Storey, S Connor, P Horgan, B Sinkinson, A Newman, D Jones
Leicester Tigers: G Murphy; S Booth, L Lloyd, R Kafer, T Stimpson; S Vesty, H Ellis; D Jelley, D West, F Tournaire, M Johnson (capt), B Kay, M Corry, N Back, A Balding
Replacements: G Chuter, D Garforth, L Deacon, J Kronfeld, L Moody, J Hamilton, G Gelderbloom