Press Association Sport understands the Reds are interested in the England under-21 international, while Tottenham Hotspur is also reported to be tracking the 22-year-old and Sociedad manager David Moyes watched the forward against Liverpool at Turf Moor on Boxing Day.
Ings is out of contract in the northern summer but the risk of waiting until then would more than likely spark a bidding war between a number of clubs in relation to the player's wages - something in which Liverpool would struggle to compete.
Under FIFA rules regarding young players, Burnley is entitled to compensation even if Ings runs down his current deal, but it is understood Sociedad would only be liable to pay £300,000 ($584,800) - leaving it plenty of room to offer a huge salary - while fellow English clubs could end up paying a fee 10 times that amount.
For that reason Liverpool has looked at the option of buying Ings now and loaning him back to Burnley for the remainder of the season.
That could potentially cost anywhere from £3million to £5million and Liverpool has already shown it is prepared to enter such arrangements after their £10million purchase of young Belgium striker Divock Origi last summer contained an agreement for him to remain at Lille on loan for the season.