The Leicester City goalkeeper emerged as a potential target for the Reds as doubts persist over the abilities of both Loris Karius and Simon Mignolet.
Cresswell, who has started featuring regularly in the starting eleven after returning from an injury, said his side hope to rise in the Premier League table in the new year.
"We won't sell Kasper until any circumstances".
Schmeichel, 29, returned to the Leicester team earlier this month after being sidelined due to a fractured hand sustained while playing against FC Copenhagen in the UEFA Champions League in mid-November.
"We are unhappy. No-one is happy, but everyone - the chairman me, players, sporting director - we have to react as soon as possible and be a strong dressing room and show all the good things on the pitch". We need the points.
Reigning PFA Player of the Year Mahrez, 25, has not enjoyed the same success as last season as he has scored three goals and provided three assists in 18 Premier League outings, as opposed to 17 goals and 10 assists for 2015/16.
"We want to reach 20 points, we have to win against West Ham. No chance. Liverpool can win the title without Kasper".
"We have to react, concentrate 100 per cent and fight".
For some reason, Leicester manager Claudio Ranieri thought it was necessary to directly respond to that rather absurd report. "We have to win, we have to win, we have to win".
Nevertheless, West Ham's Croatian chief urged his own side to continue their superb form of late, adding: "I want to build on the performance, especially the recent one against Swansea, that was really good and not to lose confidence".