Liverpool are also desperate of winning the league and they can also achieve it, if they remain consistent and Arsenal drops point. Manchester city have always been the patient dog, waiting for any mistakes from these two clubs from past years, and before you know it, they have taken advantage of their mistakes, and City will immediately top the table. Assuming it is City that is on top, I don't think that any club can take it from them.
The despiracy that Liverpool is currently having may not work for them because desperation is only going to lead them to more failures and we've seen how they've been able they've not been able to secure a win with Manchester United and the other team they played with. Reason being that it is scary for them right now to have lost that first position they were holding because it's key for them to be able to maintain that position that they were holding.
Losing it to Arsenal once again will only pose more danger to Liverpool and if care is not taken even Manchester City is likely to win over them. So what I want Liverpool to do right now is to stay more focused on delivery and not necessarily on the title because that's going to cause them more anxiety and it will enhance their failure. If they want to win they have to leave the desperation in them and focus on re-strategizing their ideas to win each and every match that they play even if it is one goal ahead of the opponent that would make Liverpool to go further and farther in the subsequent matches to come.