The former Liverpool hero says the Belgian has a debt to the Toffees and that joining a side competing for Europe would be a "cop-out".
Lukaku has been one of few shining lights on the blue side of the city this season in an underwhelming season for the Toffees, netting 25 goals in all competitions, a personal-best return in his career.
That form, and the fact it has not been mirrored by Everton as a whole, has seen the Belgian striker heavily linked with a move away to one of England or Europe's top clubs this summer.
Aldridge, who won the league title and FA Cup with Liverpool in the late 1980s, might have been expected to encourage his former club's rivals to lose their best players in the summer.
However, the 57-year-old instead insisted to 888sport that Lukaku owes it to the Toffees to turn down a "cop-out" transfer to a Champions League club, and stressed that if the 22-year-old were to move to Manchester United in particular he would risk alienating his adoring fans.
Aldridge said: "[Everton] should be higher in the table and without Lukaku’s twenty goals where would they be?
"From the city of Liverpool’s point of view the Evertonians won’t be happy when Manchester United is mentioned. He wants Champions League yes but unfortunately players today use the Champions League as a cop-out when they want to leave clubs.
"They do really well and then it’s an easy cop-out and for the clubs it’s something you have to swallow. Luis Suarez and lots of other players have done it before him but Lukaku owes Everton big-time. Unfortunately he’s not a scouser like Steven Gerrard was so he will leave if Everton get the right price for him."
It is unclear why exactly Aldridge believes Lukaku owes a debt to Everton; since he was signed from Chelsea, initially on loan in 2013 before a club-record £28 million a year later, he has contributed 61 goals in 121 games for the club.
His exit, though likely to command a considerably higher fee than the one paid by the Toffees two years ago, would be a huge blow for a club which is already struggling to re-establish itself as a top-half side under Roberto Martinez.