Bhagavata is considered natural commentary on Vedanta Sutra.
This is what Jiva Goswami says in Tattva sandarbha, text 21:
Garuḍa Purāṇa says:(quoted by Madhva in his commentary on SB 1.1.1)
pūrṇaḥ so’yam atiśayaḥ | artho’yaṁ brahma-sūtrāṇāṁ
bhāratārtha-vinirṇayaḥ || gāyatrī-bhāṣya-rūpo’sau
vedārtha-paribṛṁhitaḥ | purāṇānāṁ sāma-rūpaḥ sākṣād-bhagavatoditaḥ ||
dvādaśa-skandha-yukto’yaṁ śatavic-cheda-saṁyutaḥ |
grantho’ṣṭādaśa-sāhasraḥ śrīmad-bhāgavatābhidhaḥ ||
This work is most
complete. It expresses the meaning of the Brahma-sūtras and
Mahābhārata. It is the explanation of gāyatrī and reinforces the
meaning of the Vedas. It is the Sāma Veda among the Purāṇas and has
arisen directly from the Lord. It has twelve volumes and hundred
divisions. It has eighteen thousand verses. It is called
Jiva Goswami explains the words 'artho'yam brahmasutranam' as follows:
It is the meaning of the Brahma-sūtras. This means it is the natural
commentary on the sutras. Previously it appeared in his mind in a
subtle form. Abbreviated, it appeared again as the sutras. Later it
appeared as Bhāgavatam with great details. Though this is the
self-evident commentary on the sūtras, other recent commentaries made
by independent thinking are to be respected if they follow the
What he says is that modern commentators on Vedanta will be taken seriously to the extent they agree with Bhagavata conclusions.
Since, the very first verse of Bhagavata contains phrases like janmadasya yatah, dhimahi. It has Vedantic import and Jiva goswami uses this verse to show how the seeds of Vedanta are there in bhagavatam. Here, he uses other commentators of Vedanta Sutras' explanations to show that they can derived from first verse of bhagavatam. He doesn't use Bhagavatam as commentary of Brahma Sutras, he uses the explanations of other commentaries wherever they are in line with Bhagavatam to show how those ideas lie in first verse of bhagavatam.
oṁ namo bhagavate vāsudevāya
janmādy asya yato ’nvayād itarataś
cārtheṣv abhijñaḥ svarāṭ tene brahma hṛdā ya ādi-kavaye muhyanti yat
sūrayaḥ tejo-vāri-mṛdāṁ yathā vinimayo yatra tri-sargo ’mṛṣā dhāmnā
svena sadā nirasta-kuhakaṁ satyaṁ paraṁ dhīmahi
Here are some things he explained on the basis of first verse of Bhagavatam.
The correlation between first 5 sutras of Brahma Sutras and first verse of Bhagavata.
Vedantic discussions based on first verse of Bhagavatam:
Correlation between Upanishadic passage and first verse of Bhagavatam:
The correlation between Brahma Gayatri and first verse of Bhagavatam:
The correlation between names of chapters of Brahma Sutra and first verse of Bhagavatam:
This discussion he does at the end of Paramatma Sandarbha, apart from that he doesn't enter into Vedanta discussion.
As the other user pointed out, there are modern works however which try to correlate Bhagavatam verses with Vedanta Sutras based on Govinda Bhasya of Baladeva Vidyabhusana.
You may download it from Vedanta Sutra Srimad Bhagavatam Commentary. It does a good job of putting together English translations of Vedanta Sutra aphorisms along with English translations of each corresponding Bhagavata verse(s)