Use `tr` with its `-s` option to compress consecutive spaces into single spaces and then `grep` the result of that:
$ echo 'Some spacious string' | tr -s ' ' | grep 'Some spacious string'
Some spacious string
This would however not remove flanking spaces completely, only compress them into a single space at either end.
Using `sed` to remove the flanking blanks as well as compressing the internal blanks to single spaces:
echo ' Some spacious string' |
sed 's/^[[:blank:]]*//; s/[[:blank:]]*$//; s/[[:blank:]]\{1,\}/ /g'
This could then be passed through to `grep`.