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.
The good news for Inter Milan is Lukaku is it seems he likes to play there instead of earning more money because Al Hilal offered him 45m which is a high amount and that's not something he can get into the European teams while he still wants to play for Inter Milan, but even Inter Milan should have some negotiations with Chelsea to buy this player and considering his age they can't pay high amount of money for this player.