No, it is not possible. Actually, Dark Energy can neither be repulsion from inside, nor attraction from outside. (Outside attraction is ruled out by Anna V's comment anyway).
There is an observational evidence for the above. That evidence is in the expansion rate of universe which exceeds speed of light at large enough distances. Any attraction, or repulsion would be eventually a force (gravity included, see next para) and could not make the "universe expand" (objects move wrt one another), at FTL inside space, if we were to go by relativity.
Therefore, it can neither be internal repulsion, nor be external attraction, it has to be just expansion of space itself.
I mentioned gravity in context of attraction and repulsion because - if gravity (given sufficient distance to accelerate) was capable of accelerating something to FTL, then we know that escape speed from a black hole is $c$. That would also be ~speed at which a free falling object would enter the event horizon. Therefore if we were to shoot an object towards event horizon with fast speed, then it may have been possible for that object to attain FTL speeds prior to reaching EH, which is prohibited by relativity. I have not done any calculations about it but it seems at least with the help of slingshots with multiple black holes, it could have been possible for an object to attain FTL. Which goes against relativity as far as I know.
One more point to note is that the expansion of universe has been accelerating only for last ~5 billion years. Before that it was a slowing expansion. As we know for sure that it started out as accelerated expansion at big bang. So we already know that the expansion has switched from accelerating, to slowing down and then again to accelerating. Therefore the expansion is fluctuating between accelerating, and slowing down. Given the age of universe as 14 billion years and already two switches taken place, 5*3 = 15. In a billion years or so, it may again switch to slowing down expansion.
This fluctuation between accelerating, and slowing down of expansion suggests that both - inside attraction, and outside repulsion can be ruled out.