Lukaku went over on his ankle during the first half of Tuesday's disaster at Anfield after colliding with Gareth Barry and had to be stretchered off.
There were initial fears he had suffered ligament damage, possibly ruling him out for several months. That sparked rumours Martinez could make a late bid for a striker, with Marseille's Saber Khalifa and Lyon's Bafetimbi Gomis named as potential targets
Khalifa, a Turkey international, is reportedly available for loan while Gomis may be allowed to leave Lyon for a cut-price £3million as he only has six months remaining on his contract.
However, Everton were boosted yesterday by the news that Lukaku's injury was not as bad as first feared and could be back playing within a month.
Fellow striker Traore, who was formally introduced to the media on Thursday, is also nearing fitness after a hamstring injury and could be in contention within 10 days.
Given Traore has not played since October, he would represent a rare pair of fresh legs among the weary troops at Finch Farm.
When asked about his striking options, Martinez gave a positive assessment:
"Romelu will be back well before the final seven or eight games of the season, which is very positive.
"We had very good news in that respect. The structure of the ankle is fine and he sustained no ligament damage. It is badly, badly bruised but it is not a matter of months as we expected.
"We will see how he reacts to the next 48 hours of treatment and we will then see what the best solution is to get him back fit as quickly as possible.
We won't rush Lacina. What's important is that he becomes a key player for the end of the season and the run-in."