Avast, although called an Anti-Virus also detects malware, though no program gives 100% detection.
This sounds more like a 'Scam' than malware as such. No doubt the telephone number would either be a premium rate or seek to have remote control over your computer, which no doubt would say there are problems and seek payment to fix them.
Are you getting this regularly, e.g. when visiting a certain site, when you open your browser (which one), or using a certain program ?
A screenshot of the notice could help.
What avast program version are you using ?
What is your operating system ?
Do you have any other security programs installed ?