According to Transfermart's statistics, Neuer has achieved the most clean sheets in the Champions League history. 

Most Clean Sheets by goalkeeper in the Champions League:

1. Neuer 64 cleans sheets in 158 games

2. Casillas 59 clean sheets in 177 games

3. Buffon 53 clean sheets in 124 games

4. Van der Sar 51 clean sheets in 98 games

5. Cech 49 games in 111 games

6. Valdes 45 games in 106 games

7. Oblak 36 clean sheets in 104 games

8. Dida 35 clean sheets in 72 games

9. Courtois 34 clean sheets in 99 games

10. Kahn 34 clean sheets in 103 games