Not even sure he's the kind of Striker Pochetino wants.
That's what I think too, Chelsea rejected Inter Milan's loan extension offer not because they wanted to use Lukaku to be included in Pochettino's squad list but to avoid the opportunity to lose more if they don't sell him this season because the price is decreasing because he will get older plus his performance is not as good as expected so it will be difficult for Chelsea to sell him next season, so they are like forcing Inter to buy this player if they still want him, but unfortunately, it seems that money is an obstacle for Inter to buy this player or it could be that Inter only sees Lukaku as such a good reserve player that didn't feel the need to spend money to get him.
Clarity about this player is still a question mark, I see that the 2 teams that are in touch with Lukaku at the moment don't really want Lukaku. They can use it, but when it comes to spending money they seem to prefer other players. On the one hand, Chelsea also didn't want their losses to continue, because they brought in Lukaku not at a small cost, but he couldn't make a good contribution. On the other hand, Inter Milan may only want him as a player on loan, because it costs more to make him their permanent player.