Telephone calls to family and friends on Christmas Day may keep the phone companies busier than ever this year.

American Telephone & Telegraph Co. anticipates handling about 44.6 million calls today, which would set a holiday record. Last Christmas, the long-distance leader placed about 39.3 million calls on its lines.

MCI Communications Corp., the nation's second-largest long-distance company, expects to handle about 10 million calls on its lines Christmas Day and US Sprint Communications Co., No. 3 in the industry, anticipates as many as 15 million calls on its lines.

All three companies will have discounted holiday rates in effect during Christmas Day.

AT&T advises callers they can save money by avoiding operator-assisted calls, by dialing directly whenever possible and using a telephone credit card.

The cheapest calling times for AT&T, when rates are discounted 53 percent, are from 11 p.m. Christmas Eve until 8 a.m. Christmas Day, and from 11 p.m. Christmas Day until 5 p.m. Sunday. Evening rates, discounted 38 percent, will be in effect from 8 a.m. to 11 p.m. Christmas day.

Call volume is traditionally lowest on the holiday between 2 p.m. and 6 p.m., AT&T said.