The controversial striker looks certain to miss the Baggies' home clash with Liverpool on Sunday after being forced off early in his side's remarkable 4-3 loss at Aston Villa with a badly gashed knee.
Albion are unsure how long the veteran forward may be out with the problem but they are also well aware he also faces a possible ban.
Anelka was charged by the Football Association last week after performing the 'quenelle' gesture in December and he faces a disciplinary hearing in the coming weeks.
Mel said: "One result doesn't change the opinion about the squad but if we have the chance to sign a player during the transfer window I believe we should do.
"We must try to work to solve the problem that the injury or the ban to Anelka would cause."
Anelka was hurt as he challenged for the ball to create a chance for team-mate James Morrison during a dramatic first half in which the sides shared six goals.
Mel said: "He has had a lot of stitches to his knee. We don't know (how serious it is). Tomorrow we will know more."
Mel was frustrated that his side failed to win the keenly-contested derby after racing into a 2-0 lead inside nine minutes through Chris Brunt and a Fabian Delph own goal.
Villa replied quickly through Andreas Weimann, Leandro Bacuna and Delph and then won it with a second-half Christian Benteke penalty after Youssouf Mulumbu equalised.
Asked if his side threw the game away, Mel said: "Yes, of course.
"The start of the game was good for us. It is incredible to score three goals away and get no points."
West Brom did piece together some good attacks and dominated possession in the second half but they were undone by some poor defending.
Mel, still awaiting his first win, said: "I think we need to improve on mistakes. For example the first goal was a mistake.
"But I believe our problem in this game was Benteke and not so much our defence.
"We worked all week on the direct play of Aston Villa and I think this was our problem."
Mel thought his side should have had a penalty after Morgan Amalfitano, who was booked for diving, tangled with Ciaran Clark.
He said: "For me it was the same as the other box, but the referee is the boss."
Villa manager Paul Lambert thought his side showed a new level of maturity as they recovered from a poor start to claim only their third home win of the season in the Barclays Premier League.
He said: "To be 2-0 down in any game after eight minutes or whatever is tough but in a derby game it doubles, because of the importance to the crowd.
"But the turnaround was fantastic. What a performance that was. To turn it around the way we did was fantastic.
"You never lose faith. It was important we kept a level head and tried to get ourselves back into it.
"We showed a lot of maturity in doing that. I think they grew up a lot by doing that, especially against their rivals.
"That is the magnitude of it and it was great."
The importance of the game to fans was apparent as one ran to celebrate Villa's third goal with Lambert, but the Scot ushered him back to the stand.
He said: "A guy ran down. I think he was just enjoying the comeback.
"It was incredible, especially in a derby game, which is so different from a normal league game."
Lambert may also strengthen before Friday's transfer deadline.
He said: "There are about 15 things I am trying to do at the minute. If one comes off, great - if none come off, then it's fine.
But as for rumours linking the club with Spurs' Lewis Holtby, he said: "No - I've not heard that one."