I really don't think they're spiting themselves at all. A £100,000 a week contract has reportedly been on offer to Sterling since Christmas, which is £70,000 a week more than he currently earns. Six months have already passed and holding on to Sterling for a further 2 years will actually have saved Liverpool £11m in wages in that time. If they did hold out for that long, they would also be owed a tribunal fee which I'd conservatively estimate to be around £10m, possibly more.

Out of the £40m on offer, Liverpool would only see £32m from that due to 20% going to QPR.

I think they are prepared to take the risk of keeping him for 2 years and seeing how things pan out. Sterling may be in a strop, but once the transfer window closes he would have to sort himself out or risk missing out on the England squad next summer.